8830 PDF
8830 PDF
8830 PDF
PhD THESIS
ADANA, 2012
ÇUKUROVA UNIVERSITY
INSTITUTE OF NATURAL AND APPLIED SCIENCES
PhD THESIS
We certify that the thesis titled above was reviewed and approved for the award of
degree of the Doctor of Philosophy by the board of jury on 24/12/2012.
…………………...……... ………...............................
Assoc. Prof. Dr. İlyas EKER Assoc. Prof. Dr. Ulus ÇEVİK
MEMBER MEMBER
This Ph.D. Thesis is written at the Institute of Natural and Applied Sciences of
Çukurova University.
Registration Number:
Note: The usage of the presented specific declarations, tables, figures and photographs either in this
thesis or in any other reference without citation is subject to "The law of Arts and Intellectual
Products" number of 5846 of Turkish Republic.
ABSTRACT
PhD THESIS
ÇUKUROVA UNIVERSITY
INSTITUTE OF NATURAL AND APPLIED SCIENCES
DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING
I
ÖZ
DOKTORA TEZİ
ÇUKUROVA ÜNİVERSİTESİ
FEN BİLİMLERİ ENSTİTÜSÜ
ELEKTRİK ELEKTRONİK MÜHENDİSLİĞİ ANABİLİM DALI
II
ACKNOWLEDGEMENTS
III
CONTENTS PAGE
ABSTRACT ............................................................................................................. I
ÖZ ........................................................................................................................... II
ACKNOWLEDGEMENTS .................................................................................... III
CONTENTS ...........................................................................................................IV
LIST OF TABLES..................................................................................................XI
LIST OF FIGURES ............................................................................................. XIII
LIST OF SYMBOLS ......................................................................................... XVII
LIST OF ABBREVIATIONS .............................................................................. XXI
1. INTRODUCTION ............................................................................................... 1
1.1. Motivation for the Thesis .............................................................................. 3
1.2. Objectives of the Thesis ................................................................................ 4
1.3. Contributions of the Thesis ............................................................................ 5
1.4. General Outline ............................................................................................. 5
2. OVERVIEW OF FACTS DEVICES .................................................................... 7
2.1. Background on Alternating Current Power Transmission .............................. 7
2.1.1. Thermal Limit .................................................................................... 7
2.1.2. Maximum Power Transfer.................................................................. 7
2.1.3. Angle Stability ................................................................................... 8
2.1.4. Voltage Stability ................................................................................ 9
2.1.5. Transmission Line Loadability Characteristics ................................. 10
2.2. Classification of FACTS Devices ................................................................ 11
2.2.1. Static VAR Compensator (SVC) ...................................................... 13
2.2.2. Thyristor Controlled Series Capacitor/Compensator (TCSC)............ 15
2.2.3. Thyristor Controlled Phase Angle Regulator (TCPAR) .................... 16
2.2.4. Static Synchronous Compensator (STATCOM) ............................... 17
2.2.5. Static Series Synchronous Compensator (SSSC) .............................. 18
2.2.6. Unified Power Flow Controller (UPFC) ........................................... 19
2.2.7. Interline Power Flow Controller (IPFC) ........................................... 20
2.2.8. Generalized Unified Power Flow Controller (GUPFC) ..................... 21
IV
2.2.9. Back-to-Back STATCOM (BtB-STATCOM) ................................ 22
2.3. More Control Degrees of Freedom .............................................................. 23
2.4. Recent Advances in Power Semiconductors ................................................ 25
2.5. Field Applications of FACTS Devices at Transmission Level ..................... 25
2.6. Summary..................................................................................................... 27
3. STEADY-STATE MODELING......................................................................... 29
3.1. Introduction................................................................................................. 29
3.2. Proposed Steady-state Modeling Approach.................................................. 30
3.2.1. Configurable Multi-Converter FACTS Device................................... 31
3.2.2. Operating Constraints ........................................................................ 33
3.2.3. Control Constraints............................................................................ 35
3.2.3.1. Direct Control Mode .............................................................. 35
3.2.3.2. Indirect Control Mode............................................................ 36
3.3. Modeling in PSCAD ................................................................................... 37
3.3.1. Power Circuit .................................................................................... 37
3.3.2. Control Circuit .................................................................................. 37
3.4. Power Flow Studies ..................................................................................... 39
3.4.1. Test Systems ..................................................................................... 39
3.4.2. WSCC 3-Machine 9-Bus System ....................................................... 42
3.4.2.1. Case 1: STATCOM and SSSC Operations ............................. 42
3.4.2.2. Case 2: UPFC Operation ........................................................ 45
3.4.2.3. Case 3: IPFC Operation ......................................................... 45
3.4.2.4. Case 4: GUPFC Operation ..................................................... 47
3.4.2.5. Discussion of Simulation Results ........................................... 48
3.4.3. IEEE 14-Bus System ......................................................................... 49
3.4.3.1. Case 1: UPFC Operation ........................................................ 49
3.4.3.2. Case 2: IPFC Operation ......................................................... 51
3.4.3.3. Case 3: GUPFC Operation ..................................................... 51
3.4.3.4. Discussion of Simulation Results ........................................... 51
3.4.4. 3-Machine 7-Bus System ................................................................... 52
3.4.4.1. Case 1: Reactive Power-Voltage (Q-V) Characteristics .......... 52
V
3.4.4.2. Case 2: Real Power-Voltage (P-V) Characteristics ................. 54
3.4.4.3. Discussion of Simulation Results ........................................... 56
3.5. Summary..................................................................................................... 57
4. VOLTAGE SOURCE CONVERTER DESIGN ................................................. 59
4.1. Introduction................................................................................................. 59
4.2. Six-pulse VSC ............................................................................................. 60
4.2.1. Circuit Configuration......................................................................... 60
4.2.2. Working Principle ............................................................................. 61
4.2.3. Analysis of Six-pulse VSC ................................................................ 63
4.3. Twelve-pulse VSC ...................................................................................... 65
4.3.1. Circuit Configuration......................................................................... 65
4.3.2. Analysis of Twelve-pulse VSC .......................................................... 67
4.4. Quasi Multi-pulse VSC ............................................................................... 68
4.4.1. Circuit Configuration......................................................................... 68
4.4.2. Series Coupling Magnetic Interface ................................................... 72
4.4.3. Control Scheme for Quasi Multi-pulse VSC ...................................... 73
4.4.3.1. 2-angle Control Method ......................................................... 74
4.4.3.2. Pulse-generating Circuit......................................................... 76
4.4.4. Analysis of Quasi Multi-pulse VSC ................................................... 77
4.4.4.1. Quasi 48-pulse Operation....................................................... 77
4.4.4.2. Verification of 2-angle Control Method ................................. 79
4.5. Summary..................................................................................................... 83
5. DYNAMIC MODELING STUDIES .................................................................. 85
5.1. Introduction................................................................................................. 85
5.2. Simplex Optimization Method..................................................................... 87
5.3. Converter-Level Modeling of GUPFC ......................................................... 88
5.3.1. GUPFC Interacting with Power System ............................................. 88
5.3.2. GUPFC Controller Design ................................................................. 89
5.3.3. Finding Optimum Controller Parameters ........................................... 91
5.3.4. Simulation Studies ............................................................................. 93
5.3.4.1. Case 1: Start-up Transients .................................................... 94
VI
5.3.4.2. Case 2: Response to Real Power Flow Step Changes ............. 97
5.3.4.3. Case 3: Response to Reactive Power Flow Step Changes ..... 100
5.3.4.4. Case 4: Single-phase to Ground Fault .................................. 102
5.3.4.5. Case 5: Three-phase to Ground Fault ................................... 106
5.3.4.6. THD Content ....................................................................... 108
5.3.5. Discussion ....................................................................................... 108
5.4. Converter-Level Modeling of IPFC ........................................................... 109
5.4.1. IPFC Interacting with Power System ............................................... 109
5.4.2. IPFC Controller Design ................................................................... 110
5.4.2.1. Decoupled Controller Design ............................................... 111
5.4.2.2. Proposed Hybrid Fuzzy PI (HFPI) Controller ...................... 114
5.4.2.3. FUDE Design ...................................................................... 116
5.4.3. Finding Optimum Controller Parameters ......................................... 119
5.4.4. Simulation Studies ........................................................................... 121
5.4.4.1. Case 1 .................................................................................. 122
5.4.4.2. Case 2 .................................................................................. 124
5.4.4.3. THD Content ....................................................................... 128
5.4.5. Discussion ....................................................................................... 130
5.5. Converter-Level Modeling of BtB-STATCOM ......................................... 130
5.5.1. BtB-STATCOM Interacting with Power System.............................. 130
5.5.2. BtB-STATCOM Controller Design ................................................. 132
5.5.3. Simulation Studies ........................................................................... 133
5.5.3.1. Case1: Start-up Transients ................................................... 133
5.5.3.2. Case 2: Response to Real Power Transfer Step Changes ...... 136
5.5.3.3. Case 3: Single-phase to Ground Fault .................................. 138
5.5.3.4. Case 4: Three-phase to Ground Fault ................................... 141
5.5.3.5. THD Content ....................................................................... 143
5.5.4. Discussion ....................................................................................... 144
5.6. Summary................................................................................................... 144
6. TRANSIENT STABILITY STUDIES ............................................................. 147
6.1. Introduction............................................................................................... 147
VII
6.2. Literature Survey on Transient Stability Studies ........................................ 148
6.3. Transient Stability Improvement Using GUPFC ........................................ 149
6.3.1. Dynamic Equations for Power Generation ....................................... 149
6.3.1.1. Wind Model ........................................................................ 149
6.3.1.2. Blade Dynamics................................................................... 150
6.3.1.3. Self-excited Double Cage Induction Generator .................... 151
6.3.1.4. Salient-Pole Synchronous Generator .................................... 151
6.3.2. Power System Configuration ........................................................... 152
6.3.3. Damping Control Scheme of GUPFC .............................................. 155
6.3.3.1. Fuzzy Damping Controller (FDC)........................................ 156
6.3.3.2. Fuzzified Gain Tuner (FGT) ................................................ 157
6.3.3.3. Tuning of Scaling Factors .................................................... 158
6.3.4. Simulation Studies ........................................................................... 160
6.3.4.1. Case 1: Three-phase to Ground Fault ................................... 160
6.3.4.2. Case 2: Three-phase Fault with Longer Duration ................. 165
6.3.4.3. Case 3: Single-phase to Ground Fault .................................. 171
6.3.4.4. THD Content ....................................................................... 174
6.3.5. Discussion ....................................................................................... 174
6.4. Transient Stability Improvement Using IPFC ............................................ 175
6.4.1. Power System Configuration ........................................................... 175
6.4.2. Tuning of Scaling Factors ................................................................ 178
6.4.3. Simulation Studies ........................................................................... 178
6.4.3.1. Case 1: Three-phase to Ground Fault ................................... 180
6.4.3.2. Case 2: Two-phase to Ground Fault ..................................... 180
6.4.3.3. Case 3: Single-phase to Ground Fault .................................. 187
6.4.3.4. THD Content ....................................................................... 191
6.4.4. Discussion ....................................................................................... 192
6.5. Transient Stability Improvement using BtB-STATCOM ........................... 192
6.5.1. Power System Configuration ........................................................... 192
6.5.2. Simulation Studies ........................................................................... 194
6.5.2.1. Case 1: Three-phase to Ground Fault at Generator Bus ........ 195
VIII
6.5.2.2. Case 2: Three-phase to Ground Fault at Infinite Bus ............ 198
6.5.2.3. THD Content ....................................................................... 201
6.5.3. Discussion ....................................................................................... 202
6.6. Summary................................................................................................... 202
7. CONCLUSIONS AND FUTURE WORK........................................................ 205
REFERENCES ..................................................................................................... 211
CIRRICULUM VITAE ........................................................................................ 227
APPENDIX A: Converter Design Data for Power Flow Studies ..... Hata! Yer işareti
tanımlanmamış.
APPENDIX B: Test Systems Data ...................... Hata! Yer işareti tanımlanmamış.
APPENDIX C: PI Controller Parameters ............ Hata! Yer işareti tanımlanmamış.
APPENDIX D: Derivation of Maximum Power Injections for BtB-STATCOM Hata!
Yer işareti tanımlanmamış.
APPENDIX E: Programming Scripts .................. Hata! Yer işareti tanımlanmamış.
IX
X
LIST OF TABLES PAGE
Table 2.1. Overview of major FACTS devices with their attributes ......................... 14
Table 3.1. Flexible configuration of the multi-converter FACTS device .................. 32
Table 3.2. Operating constraints of the multi-converter FACTS device ................... 34
Table 3.3. Power flow results for voltage magnitude regulation @ 1.0 pu ............... 44
Table 3.4. Power flow results for real power regulation of Line 4-5 ........................ 44
Table 3.5. Power flow results for reactive power flow regulation of Line 4-6 .......... 45
Table 3.6. Parameters of the UPFC under different power flow control strategies ... 49
Table 3.7. Parameters of the IPFC under different power flow control strategies ..... 51
Table 3.8. Parameters of the GUPFC under different power flow control strategies 52
Table 3.9. Q-V characteristics of the two converters ............................................... 54
Table 4.1. Number of pulse-generating circuits per multi-converter FACTS device 77
Table 5.1. Simplex optimized controller parameters of GUPFC .............................. 93
Table 5.2. THD values .......................................................................................... 108
Table 5.3. Rule base for ΔVQ................................................................................. 117
Table 5.4. Simplex optimized controller parameters of IPFC ................................ 121
Table 5.5. Quantitative performance analysis of different controllers .................... 129
Table 5.6. THD values in case of three control schemes ........................................ 130
Table 5.7. THD values .......................................................................................... 143
Table 6.1. Optimization results of scaling factors .................................................. 160
Table 6.2. THD values of power system bus voltages ........................................... 174
Table 6.3. Optimization results of scaling factors .................................................. 179
Table 6.4. THD values of power system bus voltages ........................................... 191
Table 6.5. THD values of power system bus voltages ........................................... 202
XI
XII
LIST OF FIGURES PAGE
XIII
Figure 4.1. Power circuit of three-phase six-pulse VSC......................................... 61
Figure 4.2. Four quadrant VSC operation .............................................................. 62
Figure 4.3. Simulated phase-to-neutral voltage waveforms of six-pulse VSC ........ 63
Figure 4.4. Simulated phase-to-phase voltage waveforms of six-pulse VSC .......... 64
Figure 4.5. Gating signals of GTOs for 180-degrees conduction ........................... 65
Figure 4.6. Harmonic spectrum of VAB for six-pulse VSC ..................................... 65
Figure 4.7. Power circuit of three-phase twelve-pulse VSC ................................... 66
Figure 4.8. Simulated phase-to-phase voltage waveforms of twelve-pulse VSC .... 67
Figure 4.9. Harmonic spectrum of VAB for twelve-pulse VSC ............................... 68
Figure 4.10. Power circuit configuration of three-phase quasi multi-pulse VSC ...... 70
Figure 4.11. PSCAD implementation of ¼ of quasi multi-pulse VSC ...................... 71
Figure 4.12. PSCAD implementation of magnetic interfaces ................................... 72
Figure 4.13. PSCAD implementation of series coupling magnetic interface ............ 73
Figure 4.14. Voltage vectors of converters M and N in rotating reference frame ..... 74
Figure 4.15. PSCAD implementation of equations (4.5) and (4.6) ........................... 75
Figure 4.16. PSCAD implementation of switching logic for six-pulse VSC ............ 76
Figure 4.17. Simulated voltage waveforms of quasi 48-pulse VSC.......................... 78
Figure 4.18. Harmonic spectrum of VAB for quasi 48-pulse operation ..................... 78
Figure 4.19. Four quadrant operation of the proposed quasi multi-pulse VSC ......... 81
Figure 4.20. Flexible magnitude/phase angle controlled quasi multi-pulse VSC ...... 82
Figure 5.1. Flow chart of the simplex optimization method in PSCAD .................. 88
Figure 5.2. WSCC 3-Machine 9-Bus System embedded with GUPFC................... 89
Figure 5.3. Control loops of GUPFC ..................................................................... 90
Figure 5.4. PSCAD implementation of simplex method ........................................ 92
Figure 5.5. Convergence performance of cost function in simplex method ............ 93
Figure 5.6. Simulated waveforms of case 1 ........................................................... 97
Figure 5.7. Simulated waveforms of case 2 ........................................................... 99
Figure 5.8. Simulated waveforms of case 3 ......................................................... 102
Figure 5.9. Simulated waveforms of case 4 ......................................................... 105
Figure 5.10. Simulated waveforms of case 5 ......................................................... 108
Figure 5.11. 4-Machine 4-Bus System embedded with IPFC ................................. 110
XIV
Figure 5.12. PSCAD implementation of PI+DG controllers ................................... 113
Figure 5.13. PSCAD implementation of HFPI controller ........................................ 114
Figure 5.14. PSCAD-MATLAB interface ............................................................. 115
Figure 5.15. PSCAD implementation of SEPOCHDET ......................................... 115
Figure 5.16. Universe of Discourse ....................................................................... 116
Figure 5.17. MFs for FUDE output set .................................................................. 117
Figure 5.18. Control surfaces of the proposed FUDE ............................................ 118
Figure 5.19. Conceptual control configurations for the master VSC ........................ 119
Figure 5.20. Control scheme for the slave VSC ...................................................... 119
Figure 5.21. PSCAD implementation of simplex method ...................................... 120
Figure 5.22. Cost function minimization in simplex method ................................... 120
Figure 5.23. Dynamic performances of real power flow controllers ...................... 123
Figure 5.24. Dynamic performances of reactive power flow controllers ................ 125
Figure 5.25. Dynamic performance of real power flow controller for slave VSC ... 125
Figure 5.26. Dynamic performance of DC voltage controller for slave VSC ......... 126
Figure 5.27. d-q components of master VSC injected current ................................ 126
Figure 5.28. d-q components of master VSC voltage by HFPI controller............... 126
Figure 5.29. Anode-to-cathode voltage of a selected GTO in converter M ............ 127
Figure 5.30. Dynamic performances of real power flow controllers ...................... 127
Figure 5.31. Dynamic performances of reactive power flow controllers ................ 129
Figure 5.32. 3-Machine 7-Bus System embedded with BtB-STATCOM ............... 131
Figure 5.33. Control loops of BtB-STATCOM ..................................................... 132
Figure 5.34. Simulated waveforms of case 1 ......................................................... 135
Figure 5.35. Simulated waveforms of case 2 ......................................................... 138
Figure 5.36. Simulated waveforms of case 3 ......................................................... 140
Figure 5.37. Simulated waveforms of case 4 ......................................................... 143
Figure 6.1. Power system configuration embedded with GUPFC ........................ 153
Figure 6.2. PSCAD-MATLAB interface ............................................................. 154
Figure 6.3. Membership functions and fuzzy rules for STFDC ............................ 157
Figure 6.4. Control surfaces of the proposed STFDC .......................................... 158
Figure 6.5. PSCAD implementation of simplex method ...................................... 159
XV
Figure 6.6. Convergence performance of cost function in simplex method .......... 159
Figure 6.7. Simulated STFDC performance against three-phase fault .................. 164
Figure 6.8. Simulated voltage and current waveforms of GUPFC converters....... 165
Figure 6.9. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage ....... 165
Figure 6.10. Simulated STFDC performance against longer three-phase fault ....... 169
Figure 6.11. Power fluctuations following three-phase fault .................................. 170
Figure 6.12. Simulated STFDC performance against single-phase to ground fault . 174
Figure 6.13. Two-Area System embedded with IPFC and its control scheme ........ 176
Figure 6.14. PSCAD-MATLAB interface ............................................................. 177
Figure 6.15. Cost function minimization for both FACTS devices ........................ 179
Figure 6.16. Simulated STFDC performance following three-phase fault .............. 184
Figure 6.17. Simulated voltage and current waveforms of IPFC converters ........... 184
Figure 6.18. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage ....... 184
Figure 6.19. Simulated STFDC performance against two-phase fault .................... 187
Figure 6.20. Simulated STFDC performance against single-phase fault ................ 191
Figure 6.21. Power system configuration embedded with BtB-STATCOM ........... 193
Figure 6.22. Simulated BtB-STATCOM performance in case 1 ............................ 197
Figure 6.23. Simulated voltage and current waveforms of the converters .............. 198
Figure 6.24. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage ....... 198
Figure 6.25. Simulated BtB-STATCOM performance in case 2 ............................ 201
XVI
LIST OF SYMBOLS
* : Complex conjugate
° : Degrees
µ(i) : Membership function of the consequent of rule i
A : Blade impact area
a1-3 : Scaling factors of STFDC
bi : Center of membership function of the consequent of rule i
C : DC link capacitance
Cp : Dimensionless power coefficient
D : Damping coefficient of the SG
dX/dt : First order time derivative of the variable X
e : Internal generated voltage of the SG
e(k) : Error at sample instant k
ES : Line-to-line rms voltage of the sending-end side bus
eX : X-axis of the internal generated voltage of the SG
eXN : Line-to-neutral voltage of phase X
H : Henry
iD : D-component of the current
IL : Transmission line current
Iph : Phase current flowing into the converter
iQ : Q-component of the current
J : Inertia of the SEDCIG
j : Square root of -1
k : Number of sampling instant
Kp : Proportional gain of the PI controller
Kw : Damping gain
L : Inductance
Lm : Mutual leakage inductance of the SEDCIG
M : inertia constant of the SG
n : Harmonic order
XVII
P : Number of pole pairs
Pe : Real power flow error
Pinj,m : Injected real power of converter m
Pinj,mref : Injected real power of converter m
Pline : Real power flow of the transmission line
Plineref : Reference value of the real power flow of the transmission line
Ploss,m : Real power loss of converter m
PR : Receiving-end real power
PRMAX : Maximum power transfer of receiving-end side at unity power factor
Ptransfer,m : Transmitted real power of converter m from other converter(s)
PW : Mechanical power extracted from the wind
Qe : Reactive power flow error
Qinj,m : Injected reactive power of converter m
Qinj,mref : Reference value of injected reactive power of converter m
Qline : Reactive power flow of the transmission line
Qlineref : Reference value of the reactive power flow of the transmission line
QR : Receiving-end reactive power
Ra : Armature resistance
RC : Common end-ring resistance of the SEDCIG
RL : Transmission line resistance
RLD : Per-phase resistance of the three-phase load
Rs : Internal resistance of the DC voltage source
s : Laplace operator
Sline : Complex power flow of the transmission line
t : Time
T : Total simulation time
TE : Electrical torque of the SG or SEDCIG
TL : Load torque of the SEDCIG
TM : Mechanical torque of the SG
TX : X-axis time constant of the SG
Vbus : Line-to-line rms voltage of local bus
XVIII
Vbusref : Reference value of line-to-line rms voltage of local bus
Vconv : Line-to-neutral rms voltage of converter
Vconv(max) : Maximum value of line-to-neutral rms voltage of converter
VD : D-component of the voltage
Vdc : DC link voltage
VDref : Reference value of the D-component voltage
VF : Average converter voltage
Vf : Excitation winding voltage of the SG
VM : Voltage phasor of converter M
vn : Peak value of nth voltage harmonic component
VN : Voltage phasor of converter N
VQ : Q-component of the voltage
VQref : Reference value of the Q-component voltage
VR : Line-to-line rms voltage of the receiving-end side bus
VS : Voltage phasor of the selected bus
Vse : Line-to-neutral rms voltage of series converter
Vsh : Line-to-neutral rms voltage of shunt converter
VW : Wind speed
VWB : Base or mean wind speed
VWG : Gust wind component
VWN : Noise wind component
VWR : Ramp wind component
VX : Voltage phasor of the quasi multi-pulse VSC
VXn : Phase X-to-neutral voltage of the converter
VXY : Phase X-to-Phase Y voltage of the converter
w : angular frequency
W : Watt
wa : Speed of the rotating arbitrary reference frame
wB : Blade angular velocity
wi : Speed of generator-i
wiref : Reference value of the speed of generator-i
XIX
XC : Capacitive reactance
XL : Transmission line reactance
XTCR : Impedance of TCR
XTCSC : Impedance of TCSC
XX : X-component of the reactance of the SG
α : Phase angle between VM and VX
β : Gain factor of the FGT
βp : Blade pitch angle
γ : Tip speed ratio
δ : Phase angle between VD and VX
δ : Rotor angle of the SG
ΔX : Rate of change of variable X
ζ : Thyristor firing angle (zeta)
θconv : Phase angle of line-to-neutral rms voltage of converter
θR : Phase angle of receiving-end side bus
θS : Phase angle of sending-end side bus
θse : Phase-angle of line-to-neutral rms voltage of series converter
θsh : Phase-angle of line-to-neutral rms voltage of shunt converter
μ : Micro
ρ : Air density
ΣX : Integral of variable X at sample instant k
τi : Integral time constant of the PI controller
φ : Flux linkage
ΦM : Phase angle of voltage phasor of converter M
ΦN : Phase angle of voltage phasor of converter N
Ω : Ohm
XX
LIST OF ABBREVIATIONS
AC : Alternating Current
BtB-STATCOM : Back-to-Back Static Synchronous Compensator
CPU : Central Processing Unit
DC : Direct Current
DFIG : Doubly Fed Induction Generator
EMTDC : Electromagnetic Transients including Direct Current
FACTS : Flexible Alternating Current Transmission Systems
FDC : Fuzzy Damping Controller
FGT : Fuzzified Gain Tuner
FUDE : Fuzzy Decoupler
GCT : Gate Commutated Thyristor
GTO : Gate Turn-off Thyristor
GUPFC : Generalized Unified Power Flow Controller
HFPI : Hybrid Fuzzy Proportional Integral
HVDC : High Voltage Direct Current
IAE : Integral Absolute Error
IEEE : Institute of Electrical and Electronics Engineers
IGCT : Integrated Gate Commutated Thyristor
IPFC : Interline Power Flow Controller
ISE : Integral Square Error
ITAE : Integral Time Absolute Error
MF : Membership Function
MSC : Mechanically Switched Capacitor
MSR : Mechanically Switched Reactor
MVA : Mega Volt-Ampere
NR : Newton-Raphson
PI : Proportional Integral
PI+DG : Proportional Integral Control with Decoupled Gains
PLL : Phase Lock Loop
XXI
P-Q : Real Power-Reactive Power
PSCAD : Power System Computer Aided Design
PU : Per unit
P-V : Real Power-Voltage
PWM : Pulse Width Modulation
Q-V : Reactive Power-Voltage
SEDCIG : Self-excited Double Cage Induction Generator
SEPOCHDET : Set-Point Change Detector
SG : Salient-Pole Synchronous Generator
SSR : Subsynchronous Resonance
SSSC : Static Series Synchronous Compensator
STATCOM : Static Synchronous Compensator
STFDC : Self-Tuning Fuzzy Damping Controller
SVC : Static Var Compensator
TCPAR : Thyristor Controlled Phase Angle Regulator
TCR : Thyristor Controlled Reactor
TCSC : Thyristor Controlled Series Capacitor/Compensator
THD : Total Harmonic Distortion
TSC : Thyristor Switched Capacitor
TSR : Thyristor Switched Reactor
UPFC : Unified Power Flow Controller
VAR : Volt Ampere Reactive
VI : Voltage-Current
VSC : Voltage Source Converter
WSCC : Western System Coordinated Council
XXII
XXIII
1. INTRODUCTION A. Mete VURAL
1. INTRODUCTION
1
1. INTRODUCTION A. Mete VURAL
For the factors described above, it becomes evident that the operation of
power system structure under great changes is a complex and challenging
engineering task which requires efficient use of all power system elements without
disturbing technical operational limits and power systems with increasing complexity
are highly expected to be fast and real-time controlled to fulfill the requirements for
providing uninterrupted and reliable electrical energy to customers in the event of
generation and transmission outages.
Flexible Alternating Current Transmission Systems (FACTS) emerge as
“power electronic based solution” using solid-state switching devices and modern
control algorithms to increase controllability and enhance power transfer capacity of
existing transmission network. FACTS have gained greater interest during the last
decades due to the deregulation and restructuring strategies of power systems.
FACTS concept was originally proposed and conceptualized by Narain G.
Hingorani (Hingorani, 1988) and later defined formally as “alternating current
transmission systems incorporating power electronic-based and other static
controllers to enhance controllability and increase power transfer capability” by the
FACTS Terms & Definitions Task Force FACTS Working Group of the direct
current (DC) and FACTS subcommittee of Institute of Electrical and Electronics
Engineers (IEEE) (IEEE, 1997).
With the increase of voltage and current ratings of solid-state power
semiconductor devices, power electronics technology has penetrated into the area of
high voltage transmission in terms of FACTS devices (controllers) receiving great
attention to enhance power system operation by controlling one or more power
system parameters simultaneously and independently (Hingorani, 2000). During the
last two decades, FACTS devices have been proposed to enhance steady-state (static)
performance of power systems, such as increase of transmission line capacity, real
and reactive power flow control, loop-flow control, load sharing among parallel
corridors, voltage regulation, congestion management, and optimal power flow for
economic power system operation. The examples of dynamic performance
improvement include; enhancement of small signal stability and transient stability of
2
1. INTRODUCTION A. Mete VURAL
power systems by damping out oscillations, fast reactive power support for dynamic
voltage control, maintaining voltage stability, and power quality improvement.
Since the time when FACTS devices were first proposed, modeling and
control of different FACTS devices have been broadly studied. In particular, there
are extensively research results covering a wide range of applications of single-
converter FACTS devices, such as Static Synchronous Compensator (STATCOM)
and Static Series Synchronous Compensator (SSSC) in literature. Multi-converter
FACTS devices, on the other hand, has emerged as a new opportunity to cope with
the aforementioned power system problems by controlling multiple power system
variables simultaneously and independently. However, the research for multi-
converter FACTS devices is relatively narrow and limited.
There exists a lack in realistic converter models for high power high voltage
applications which takes switching of semiconductor devices into account. Generally
the studies rely on two approaches. In the first approach, a set of linearized equations
are derived using fundamental frequency model of each converter of the FACTS
device. Here the converter is modeled as controllable voltage or current source
operating with fundamental system frequency (50 or 60 Hz), under the assumption
that the harmonics are neglected. This approach may be useful for steady-state or
power flow studies. In the second approach, six-pulse elementary converters
switched at frequencies relatively higher than the system frequency are used to
approximate harmonic content and converter modulation techniques. This approach
can suffer from high switching frequencies and relatively simple converter structure
which are not suitable for high power applications. This situation has motivated to
take a deep glance into the analysis of multi-converter FACTS devices including
more realistic converter models and their advanced controls.
Multi-converter FACTS devices are multi-input multi-output non-linear
systems with operational constraints which require advanced control algorithms. On
the other hand, fuzzy set theory presents good characteristics to address complex
3
1. INTRODUCTION A. Mete VURAL
control problems and has already proven to be efficient in several planning, control,
and operation problems in power systems. The fact that the need for computational
intelligence based control techniques including optimization methods is
indispensable for high performance control of the multi-converter FACTS devices
has also motivated this work.
The need for efficient utilization of power systems is increasing day by day in
the world and in Turkey. Besides these global conditions, there is not a well-shaped
research background on multi-converter FACTS devices in Turkey. This study will
provide a strong background on this subject.
4
1. INTRODUCTION A. Mete VURAL
5
1. INTRODUCTION A. Mete VURAL
6
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
E S VR
PR = sin(θ S − θ R ) (2.1)
XL
7
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
where PR and QR are the real and reactive power flow into Bus 2, respectively. ES and
VR are the voltage magnitudes of Buses 1 and 2, respectively. θS and θR denote phase
angles of Buses 1 and 2, respectively. XL is the reactance of the transmission line
having negligible resistance and capacitance. From equation (2.1) a non-linear
power-angle relationship can be obtained as in Figure 2.2 assuming fixed XL and
fixed bus voltage magnitudes. There is a maximum limit of transmitted power when
phase shift is 90°. Under fixed bus voltages, a suitable FACTS device can increase
maximum limit of the transmitted power further by line compensation, i.e., reducing
XL effectively.
Power-angle curve in Figure 2.2 can be used to describe roughly the angle
stability of the generators in a power system without making classification. Under
steady-state conditions, there is equilibrium between input mechanical power and
output electrical power of each synchronous generator in an interconnected system
which leads to constant speed operation. When the system is perturbed for instance a
fault occurs, this equilibrium is upset, resulting in accelerating or decelerating of the
8
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
rotors of the machines. If the machine connected at Bus 1 runs faster transiently than
the other one connected at Bus 2, phase shift in equation (2.1) increases which result
in an increase of real power transfer from Bus 1 to Bus 2 acting to reduce speed error
between the machines. When phase shift increases further beyond a certain limit, real
power transfer decreases which can lead to unstable operation. Fast and robust
control algorithms for FACTS devices can solve the stability problem by real-time
control of XL and/or phase shift.
9
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
Due to the fact that voltage drop in the transmission line is a function of real
as well as reactive power flow, load power factor is prominent on the power-voltage
curves of the system. For a given power factor, real power can be transferred at two
different voltage levels. The voltage stable operation is above the dashed line
denoting locus of critical points. In another words, the system is voltage stable only
if the load bus voltage VR is near to 1.0 per-unit (pu).
Figure 2.4 shows QR-VR curves at Bus 2 for a fixed value of PR. Voltage
stability limit is reached at the critical point where dQR/dVR reaches zero. The system
is voltage stable at the right side of the locus of critical points where dQR/dVR is
positive. Stable operation at the left side of the locus of critical points can be
achieved effectively using reactive power compensation with a FACTS device
having sufficiently control range.
10
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
transmission lines for different voltage levels. In ideal, the usage of the transmission
line for real power transmission is up to its thermal limit. As line length increases,
voltage and angle stability limits determine line loading. These limits can be shifted
upward, up to the thermal limit by means of utilizing appropriate FACTS devices. It
is clear that the more line length, the more opportunity for the utilization of FACTS
devices. Needs, benefits, and the practical requirements should be examined together
to justify the investment into the appropriate FACTS device.
11
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
Depending on the connection type to the power network, FACTS devices can
be divided into five categories:
12
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
13
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
Static synchronous
Shunt compensation, voltage stability,
compensator (STATCOM)
power oscillation damping
Power flow control, voltage
Static series synchronous control, voltage stability, VAR
Series
compensator (SSSC) compensation, power oscillation
damping, SSR mitigation
Power flow control, voltage
Unified power flow Combined control, voltage stability, VAR
controller (UPFC) Shunt-Series compensation, power oscillation
damping, SSR mitigation
Multi-line power flow control,
voltage control, voltage stability,
Interline power flow Combined
VAR compensation, power
controller (IPFC) Series-Series
Multi-converter
14
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
The required rating and the specification of the SVC are determined
according to the VI characteristics of the SVC shown in Figure 2.6b. Since the
reactive power of the capacitor is directly proportional to the system voltage, a sharp
reduction of reactive power support at large voltage drops is observed during some
severe contingencies (Hingorani et al., 2000). This situation is the major drawback of
SVC applications for voltage support in power systems.
15
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
Figure 2.7. TCSC configuration: (a) typical arrangement (b) z-α characteristics
π
X TCR (ς ) = X TCR (2.2)
π − 2ς − sin ς
where XTCR=wL, and XTCR≤ XTCR(ζ)≤∞. The controllable steady-state impedance of the
TCSC at system fundamental frequency is obtained as
X C X TCR (ς )
X TCSC (ς ) = (2.3)
X TCR (ς ) − X C
where XC=1/wC. From Figure 2.7b, the resonance region is inhibited for ζ1≤ ζ≤ ζ2
where XTCR(ζ) = XC. XTCSC is generally kept below XL to avoid over-compensation of
the transmission line.
16
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
voltage v as illustrated in Figure 2.8b. This small voltage vector resulted from the other
two phases via shunt transformers is inserted in series with the transmission line. With
this addition phase angle of the system voltage is varied. Thyristor switching enables
relatively small angular adjustments making resultant angular change approximately
proportional to the injected voltage, while the magnitude of system voltage remains
almost constant (Hingorani et al., 2000).
Figure 2.8. TCPAR configuration: (a) thyrsitor arrangement (b) vector diagrams
17
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
18
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
Figure 2.10. SSSC configuration: (a) typical arrangement (b) operating modes
19
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
having phase angle equal to that of VS. Series compensation can be applied if Vpq is
inserted having phase angle that leads or lags 90° by IL. Transmission angle can be
shifted if Vpq is inserted such that desired phase shift is obtained without any change
in magnitude. Flexible operation mode shown in Figure 2.11b yields independent and
simultaneous control of real and reactive power flow on the line which cannot be
attained by single-converter FACTS devices. UPFC can also control bus voltage
where its shunt VSC is connected by reactive power injection (Gyugyi, 1995).
Figure 2.11. UPFC configuration: (a) typical arrangement (b) operating modes
20
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
Figure 2.12. IPFC configuration: (a) typical arrangement (b) operating mode
This feature is not possible either in TCSC or SSSC in which only real power
flow can be controlled. Upper VSC regulates DC link voltage by balancing real
power between VSCs and at the same time it can regulate real or reactive power flow
on the line where it is being coupled. Moreover IPFC can serve like a virtual
transmission line so that an overloaded line can be relieved by forwarding real power
flow to the underloaded line. Although IPFC and UPFC have the same number of
control degrees of freedom, IPFC has received less attention generally in literature
when compared with the UPFC based studies.
GUPFC is the extended version of UPFC with the addition of one or more
series VSC to increase power system controllability (Fardanesh et al., 2000). GUPFC
extends the concept of power flow and voltage control beyond that is achievable with
either UPFC or IPFC. GUPFC having the simplest structure consists of one shunt
VSC and two series VSCs as shown in Figure 2.13. Series VSCs can exchange real
21
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
power with two transmission lines to inject controllable voltages Vpq1 and Vpq2 with
full angle control (0°≤θ1≤360°, 0°≤θ2≤360°) that cannot be attained either UPFC or
IPFC. Shunt VSC both supports real power requirements of the series VCSs via
common DC link and provide voltage support at the bus where it is being connected.
GUPFC can control real and reactive power flows of the two parallel transmission
lines as well as bus voltage simultaneously and independently, hence it has stronger
control capabilities than UPFC. To add extra control degrees of freedom, the number
of series VSCs can be increased to control more power flows at the same time. To
relieve congestions, GUPFC may be installed in a substation to manage power flows
of multi-lines or a group of lines and provide voltage support as well. Although the
concept is not new, GUPFC has not gained much interest in literature.
Figure 2.13. GUPFC configuration: (a) typical arrangement (b) operating modes
22
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
The reactive power flow on the line in Figure 2.1 can be written in equation
(2.4). The effective change in either or the combination of the line impedance and
23
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
phase angles by the applied compensation does not only change real power flow
(equation (2.1)) but also reactive power flow is varied as well (Kundur, 1994).
Operational characteristics of UPFC, IPFC, and GUPFC can overcome this natural
real power-reactive power (P-Q) coupling phenomenon so that independent real and
reactive power flow control can be provided simultaneously. This feature cannot be
attained either by a conventional or a single-converter FACTS device.
E S VR
QR = (1 − cos(θ S − θ R )) (2.4)
XL
Independent P-Q control feature also regulates X/R ratio of the transmission
line indirectly in which conventional series compensators such as fixed capacitor,
TCSC, or SSSC only controls real power flow by varying line reactance.
Conventional series compensation which are unable to control reactive power flow
reduces only X, thus, X/R ratio is distorted significantly in which excessive amounts
of reactive power flows are observed on the compensated lines which increase line
losses significantly. Multi-converter FACTS devices, on the other hand, compensate
against resistive line voltage drop so that effective value of R is also controlled to get
a balanced X/R ratio (Hingorani et al., 2000).
Control degrees of freedom of the FACTS devices can be defined as 2n-1
where n represents number of converters being utilized. For instance, the simplest
IPFC and the simplest GUPFC can control three and five power system parameters in
a simultaneous manner, respectively.
Total MVA rating, roughly the sum of individual ratings of hardware
elements such as high power converters and coupling magnetic interface, is
effectively used in a multi-converter FACTS device. For instance, when the
operation of individual STATCOM plus SSSC is compared with that of UPFC with
the same MVA rating, the latter FACTS device provides an additional control
capability, that is the capability to control the reactive flow on the transmission line.
The independent operation of STATCOM and SSSC cannot provide this flexibility
24
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
even the sum of MVA ratings of STATCOM and SSSC is equal to that of UPFC. In
this regard, UPFC provides more control capabilities to the power system.
The development of FACTS devices has continued to grow with the growing
capabilities of power semiconductors. Silicon based thyristors is widely used in first
generation FACTS devices which have been present for several decades with voltage
rating up to 11.0 kV (Chakraborty, 2011). The applications of second generation
FACTS devices have been implemented using high power converters ranging from
10 MVA to 250 MVA. Gate turn-off thyristor (GTO), gate commutated thyristor
(GCT), and integrated gate commutated thyristor (IGCT) are the common options
with switching frequencies up to a few kHz. Silicon based GTOs have current rating
up to 10 kA with voltage rating up to 9.0 kV (Chakraborty, 2011). GCT with ratings
6 kV and 6 kA has proven itself for high power converter applications for
STATCOM (Reed et al., 2001). The performance and electrical rating of IGCT has
increased dramatically in recent years. IGCTs with ratings 4.5-10 kV and 4.0 kA-6.5
kA are available in the market (Yongsug et al., 2009). IGCT does not require snubber
circuits and has better turn-off characteristics, lower conducting and switching loss,
and simpler gate control compared with GTO. It finds an application area of high
power converters for wind power now, and seems to be a future option for extensive
application prospect, including FACTS devices (Chengsheng et al., 2009). Ongoing
semiconductor research for the next decade seems to cover mainly silicon carbide
and gallium nitride materials to increase suitability and broadened applications of
semiconductor devices in mega-watt range systems (Vobecky, 2011).
25
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
FACTS devices applied at the transmission level are listed below for the sake of
highlight:
26
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
2.6. Summary
27
2. OVERVIEW OF FACTS DEVICES A. Mete VURAL
28
3. STEADY-STATE MODELING A. Mete VURAL
3. STEADY-STATE MODELING
3.1. Introduction
Power flow (load flow) studies which require steady-state modeling are
crucial for the design and performance analysis phases of the FACTS devices
embedded in power systems. The decisions and the future expansion options are
specified based on the results obtained from power flow studies. In this chapter, an
approach for the steady-state modeling of GUPFC, IPFC, and BtB-STATCOM for
power flow studies is presented.
In power flow studies of the IPFC, each VSC is generally modeled as pure
sinusoidal three-phase balanced voltage source whose magnitude and phase angle are
controlled. This voltage source is assumed to operate at fundamental system
frequency of 50 Hz or 60 Hz and connected to the transmission line in series with a
series reactance/impedance, which represents coupling transformer. Each coupling
transformer is modeled as pure inductive reactance if converter losses are neglected
(Xuan et al., 2004), (Xia et al., 2008), (Vasquez-Arnez et al., 2008). When the losses
of the converters are taken into account, each coupling transformer is modeled as
impedance having both resistive and reactive components (Zhang, 2003),
(Bhowmick et al., 2009), (Yankui et al., 2006), (Vinkovic et al., 2011), (Natália et
al., 2012). Alternatively, series voltage source is decomposed into direct and
quadrature components which facilitates the control of the source (Vasquez-Arnez et
al., 2008). Each series converter of the IPFC is modeled as controllable impedance
inserted into the compensated line in series (Fardanesh et al., 2004).
Power flow studies of the GUPFC assumes that the shunt and the series
converters can be represented as ideal voltage sources with series
reactances/impedances when losses are ignored (Padhy et al., 2005), (Vasquez-Arnez
et al., 2008). When losses are taken into account, each series transformer is modeled
as impedance having resistive and reactive components (Zhang et al., 2001), (Zhang
et al., 2004). Discrepantly, the shunt converter of the GUPFC is modeled as current
source with series connected reactance (Vasquez-Arnez et al., 2008).
29
3. STEADY-STATE MODELING A. Mete VURAL
Power flow studies of the BtB-STATCOM is limited and have been studied
under the concept of VSC based HVDC in which shunt converters are modeled as
voltage sources with series impedances including converter losses into account
(Zhang et al., 2004), (Pizano-Martinez et al., 2007).
The inclusion of voltage/current sources provides real and reactive power
exchange between the FACTS device and the power grid at newly added ghost buses
which forms the basis of power injection models of the FACTS devices.
Conventional Newton-Raphson (NR) power flow algorithm is then modified by the
user using the set of real and reactive power injections at the buses where the FACTS
devices are located. Generally the structure of the Jacobian matrix is preserved but
Jacobian matrix formation for IPFC and GUPFC is different by taking derivatives
with respect to real and imaginary parts of the line current as opposed to
conventional approach (Vinkovic et al., 2011).
Alternatively, NR solution algorithm is accomplished by a power system
analysis software package instead of writing the codes by the user. The power
injection model of the FACTS device is then defined in a user-defined model for
power flow studies of the power systems embedded with the FACTS devices
(Tümay et al., 2004), (Vural et al., 2007). In this chapter a different steady-state
modeling approach for power flow studies of GUPFC, IPFC, and BtB-STATCOM is
proposed in PSCAD neither requires a power injection based user-defined model nor
modification of NR codes by the user is required due to real and reactive power
injections caused by the FACTS device.
30
3. STEADY-STATE MODELING A. Mete VURAL
the power system and solves both operating and control constraint equations required
for the power flow study.
31
3. STEADY-STATE MODELING A. Mete VURAL
Figure 3.2. Voltage source equivalent model of the generic FACTS device
32
3. STEADY-STATE MODELING A. Mete VURAL
0 ≤ Vconv ≤ Vconv(max)
(3.1)
0 ≤ θ conv ≤ 2π
Each converter should be fed from a constant DC link voltage for “voltage
source” based operation. DC link voltage Vdc is defined in equation (3.2) for single-
converter operation (Mode 1-4) and should be kept constant in steady-state. This
constraint is established by regulating Vdc to its reference that can be succeeded by a
closed-loop control scheme. In steady-state, time derivative of Vdc becomes zero and
equation (3.2) reduces to equation (3.3) for converter m.
dVdc
Pinj ,m + Ploss ,m = CV dc (3.2)
dt
Pinj ,m + Ploss ,m = 0
(3.3)
33
3. STEADY-STATE MODELING A. Mete VURAL
34
3. STEADY-STATE MODELING A. Mete VURAL
In direct control mode, the user sets the reference values of the real and
reactive power injections for each VSC directly in any operating mode of the FACTS
device. In steady-state, equation (3.5) can be written as a control constraint for
reactive power injection for converter m. This case is valid for all modes (Mode 1-9).
When revealing real power injection constraint, reference value of the real power
injection by converter m should be equal to the power loss of the converter in steady-
state, as written in equation (3.6). This case is valid for single-converter operation
(Mode 1-4). In multi-converter operation (Mode 5-9), reference values of the desired
real power injections become dependent upon each other. For example for UPFC-1,
equation (3.7) is derived and written as real power injection constraints for the two
converters. Equation (3.7) can be modified as equations (3.8) and (3.9) for IPFC and
GUPFC, respectively. In direct control mode, the effects of real and reactive power
injections on power system variables, such as, real and reactive power flows, real and
reactive transmission losses, bus voltage profile, can be investigated based on power
injection concept.
Ploss1 + Ploss 2 + Ploss 3 + Pinj ,1 ref + Pinj , 2 ref + P inj ,3 ref = 0 (3.9)
35
3. STEADY-STATE MODELING A. Mete VURAL
In indirect control mode, the user sets reference values of the power system
parameters such as, bus voltage and real and reactive power flows instead of direct
real and reactive power injections by VSCs. The bus voltage control constraint is
given in equation (3.10) and can be solved generally by the FACTS device having a
shunt VSC (Mode 1,2,5,6,7,9). Vbus is the voltage magnitude of the local bus, to
which shunt VSC is connected. Vbusref is the reference value of the voltage magnitude
of the local bus. In a similar manner, power flow control constraint pair given in
equation (3.11) is solved by the FACTS device having multi-converters (Mode 5-9).
Alternatively, only real or only reactive power flow constraint is required to be
solved merely, this can be established by the FACTS device having series converters
(Mode 3,4,6-9).
Apparent power constraint of any mode, given in the last column of Table 3.2, is
not supposed to be a control constraint either in direct/indirect control mode. It is not
come up to a reference value, instead it is observed explicitly and expected to be in
the limits of FACTS device rating. It can be observed that under which operating
conditions, violation of apparent power rating occurs. Real power constraints, given
in equations (3.6) and (3.9), should also be provided in indirect control mode. Either
in direct or indirect control mode, for a given control objective, required voltage
magnitude and phase angle of each converter are iteratively found in PSCAD by
updating the solution at each solution time step. Depending on the control
requirements these two control modes can be operated simultaneously.
36
3. STEADY-STATE MODELING A. Mete VURAL
37
3. STEADY-STATE MODELING A. Mete VURAL
appropriate for power flow studies, the voltage and the phase angle of the respective
converter are used as control inputs in steady-state conditions.
38
3. STEADY-STATE MODELING A. Mete VURAL
In direct control mode, reactive and real power injections by the converter m
of the FACTS device are controlled by the voltage magnitude, Vcontrolm and the
phase angle, ph_vscm, respectively as shown in Figure 3.4. After the power flow
problem has reached to a solution, PSCAD variable Vcontrolm (m=1,2,3,4) reaches
to its steady-state values of Vsh1-2, Vse1-2 and PSCAD variable ph_vscm (m=1,2,3,4)
becomes equal to the steady-state values of θsh1-2, θse1-2, respectively.
In indirect control mode, external power system parameters such as line real
and reactive power flows and/or bus voltage magnitudes are regulated at their desired
values by the control inputs of the converters. In both modes, PI controller is also
used as constraint provider, so it holds voltage magnitude and phase angle of the
converter within allowed limits. Operating constraints given in equation (3.1) are
satisfied by this means. All controlled variables are graphically displayed using
multimeter blocks in PSCAD master library.
39
3. STEADY-STATE MODELING A. Mete VURAL
40
3. STEADY-STATE MODELING A. Mete VURAL
Figure 3.5. PSCAD model of the P-Q load connected at high voltage bus
41
3. STEADY-STATE MODELING A. Mete VURAL
42
3. STEADY-STATE MODELING A. Mete VURAL
43
3. STEADY-STATE MODELING A. Mete VURAL
Table 3.3. Power flow results for voltage magnitude regulation @ 1.0 pu
Bus Uncompensated STATCOM-1 SSSC-1 SSSC-2
No, i Vi (pu) Qinj1 (pu) Qinj2 (pu) Qinj3 (pu)
4 0.9930 + 0.1272 + 0.1654 + 0.0762
5 0.9665 + 0.6423 + 0.0168 + 0.7550
6 0.9830 + 0.3359 + 0.4907 + 0.0014
7 1.0010 + 0.0050 - 0.0002 + 0.2782
8 0.9911 + 0.3893 + 0.0230 + 0.0118
9 1.0010 - 0.3434 + 2.2900 + 0.1584
Table 3.4. Power flow results for real power regulation of Line 4-5
STATCOM-1 SSSC-1 STATCOM-1 SSSC-1
P4-5ref P4-5+jQ4-5 P4-5+jQ4-5 Qinj1, Vsh1 Qinj3, Vse1
(pu) (pu) (pu, kV) (pu, kV)
- 25% 0.5987-j0.2546 0.5987+j0.1795 -3.1370, 0.10 -0.0510, 1.84
- 50% 0.3991-j0.3794 0.3991+j0.1720 -3.1720, 8.17 -0.0734, 3.81
- 75% 0.1995-j0.3955 0.1995+j0.1182 -2.4140, 4.66 -0.0621, 6.07
- 100% 0.0320-j0.1642 0.0000-j0.0050 -0.0030, 0.05 0.0013, 9.05
+ 2% 0.8142+j0.2382 0.8142+j0.1453 0.6433, 21.6 0.0050, 0.14
+ 5% 0.8382+j0.3775 0.8382+j0.1390 1.6410, 22.93 0.0133, 0.35
+ 7% 0.8541+j0.4773 0.8541+j0.1345 2.3520, 23.80 0.0189, 0.49
+ 10% 0.8781+j0.6384 0.8781+j0.1274 3.4920, 25.07 0.0278, 0.70
44
3. STEADY-STATE MODELING A. Mete VURAL
its desired values. However, Line 4-6 is regulated by STATCOM-1 at the expense of
device rating violation.
Table 3.5. Power flow results for reactive power flow regulation of Line 4-6
SSSC-2 STATCOM-1 SSSC-2
STATCOM-1
Q4-6ref P4-6+jQ4-6 Qinj1, Vsh1 Qinj3, Vse2
P4-6+jQ4-6 (pu)
(pu) (pu, kV) (pu, kV)
- 25% 0.5556+j0.0429 0.5458+j0.0429 0.8256, 21.87 0.0058, 1.20
- 50% 0.5527+j0.0286 0.5441+j0.0286 0.7109, 21.71 0.0043, 1.03
-75% 0.5498+j0.0143 0.2640+j0.0143 0.5961, 21.55 0.0305, 2.59
- 100% 0.5468+j0.0000 0.3487+j0.0000 0.4810, 21.38 0.0276, 1.78
+ 25% 0.5613+j0.0716 0.5493+j0.0716 1.0560, 22.18 0.0095, 1.55
+ 50% 0.5641+j0.0859 0.5510+j0.0859 1.1700, 22.33 0.0117, 1.72
+75% 0.5669+j0.1002 0.5528+j0.1002 1.2850, 22.48 0.0142, 1.89
+ 100% 0.5696+j0.1146 0.5547+j0.1146 1.4000, 22.63 0.0168, 2.07
IPFC (Mode 8) is positioned on Line 4-5 (VSC2) and on Line 4-6 (VSC3).
Bus 4 voltage, V4 is regulated at 1.0 pu by VSC2 while Pinj2 is regulated at -0.030 pu
to meet the losses of the converters and ensuring real power balance between them
(indirect control mode). At the same time Qinj3 is regulated at values of 0.1 pu, 0.2
pu, and 0.3 pu, respectively by VSC3 (direct control mode). Since IPFC is a two-
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3. STEADY-STATE MODELING A. Mete VURAL
VSC FACTS device, control degree of freedom is three, so that Vse2, Vse3, and θse3 are
independent control parameters. However, θse2 should be regulated to ensure real
power balance among the converters. For each regulated value of Qinj3, θse3 is altered
from 0º to 360º in small degrees to obtain P-Q control planes of Line 4-6 as shown in
Figure 3.8.
Figure 3.7. P-Q Control planes of Line 4-6 obtained with UPFC
Figure 3.8. P-Q Control planes of Line 4-6 obtained with IPFC
46
3. STEADY-STATE MODELING A. Mete VURAL
Figure 3.9. P-Q control planes of Line 4-5 obtained with GUPFC
47
3. STEADY-STATE MODELING A. Mete VURAL
Figure 3.10. P-Q control planes of Line 4-6 obtained with GUPFC
By examining Tables 3.4 and 3.5, undeterministic real and reactive power
flows are observed in both of the above tasks. This is due to the utilization of single-
converter FACTS devices which are mentioned in Section 2.3. This might necessitate
using multi-converter topologies providing multiple control degrees of freedom, if
independent real and reactive power flow regulation is required on a specific line. It
is generally concluded that STATCOM is practical for voltage regulation and SSSC
exhibits superior real and reactive power flow regulation performance than
STATCOM with smaller device rating of SSSC. It is also concluded from the
obtained P-Q circles that UPFC, IPFC, or GUPFC is able to increase/decrease real
and reactive power flows as well as reverse the direction of flow. Zero reactive
power flow can also be achieved to decrease transmission losses. The higher reactive
compensation level which means higher reactive power injection, the larger P-Q
control area is attained by the FACTS device. These results have been verified from
literature (Gyugyi et al., 1995), (Gyugyi et al., 1999). Maximum attainable reactive
compensation level for each converter is always observed under 1.0 pu because of
non-zero Ptransfer and converter losses.
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3. STEADY-STATE MODELING A. Mete VURAL
PSCAD model of IEEE 14-Bus System is shown in Figure 3.11. Power flow
control capabilities of UPFC-1 and UPFC-2 are investigated in this case study.
Uncompensated parameters of the test system are as follows: V5 = 1.020 pu, P52
+jQ52 = - 0.4074 + j0.1667 pu, and P54 + jQ54 = 0.6293 + j0.0276 pu.
First, UPFC-1 (Mode 6) is positioned at Bus 5 (VSC1) and on Line 5-2
(VSC2) in indirect control mode. Bus 5 voltage, V5 is regulated at different set points
by VSC1 while Pinj1 is regulated at -0.030 pu to meet the losses of the converters and
ensuring real power balance between them. For the given set of reference values,
power flow solution is obtained with the internal parameters of UPFC-1. The results
are listed in Table 3.6.
Secondly, UPFC-2 (Mode 7) is positioned at Bus 5 (VSC1) and on Line 5-4
(VSC3) in indirect control mode. Similarly V5 is regulated at different set points by
VSC1 while Pinj1 is regulated at -0.030 pu. For the given set of reference values,
power flow solution is obtained with the internal parameters of UPFC-2. The results
are listed in Table 3.6.
Table 3.6. Parameters of the UPFC under different power flow control strategies
UPFC-1
scheduled system variables VSC1 output voltage VSC2 output voltage
P52ref + jQ52ref V5ref magnitude (kV) phase angle (º) magnitude (kV) phase angle (º)
0.15+j0.40 1.00 12.21 -41.46 2.35 4.05
-0.20+j0.05 1.01 12.13 -39.78 0.81 17.62
-0.35+j0.15 1.01 12.16 -38.80 0.57 -35.74
-0.50-j0.15 0.95 10.39 -37.16 0.79 -82.73
UPFC-2
scheduled system variables VSC1 output voltage VSC3 output voltage
P54ref + jQ54ref V5ref magnitude (kV) phase angle (º) magnitude (kV) phase angle (º)
0.50+j0.02 1.00 12.01 -38.34 0.73 -71.10
0.80+j0.05 1.05 12.10 -39.89 0.99 -8.09
-0.20+j0.01 1.00 11.87 -35.07 2.50 -122.74
0.15-j0.025 1.015 12.25 -36.75 1.42 -122.49
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3. STEADY-STATE MODELING A. Mete VURAL
50
3. STEADY-STATE MODELING A. Mete VURAL
IPFC (Mode 8) is positioned on Line 5-2 (VSC2) and on Line 5-4 (VSC3) to
control reactive power flow of Line 5-2 and real and reactive power flows of Line 5-
4 at their desired values in indirect control mode. Pinj2 is regulated at -0.030 pu to
meet the losses of the converters and ensuring real power balance between them. For
the given reference values of the real and reactive power flows, power flow solutions
including internal parameters of IPFC are listed in Table 3.7.
Table 3.7. Parameters of the IPFC under different power flow control strategies
IPFC
scheduled system variables VSC2 output voltage VSC3 output voltage
P54ref + jQ54ref Q52ref magnitude (kV) phase angle (º) magnitude (kV) phase angle (º)
0.50+j0.10 j0.01 3.66 -141.41 1.16 29.68
0.65+j0.008 j0.08 0.68 -109.69 0.35 68.06
-0.20+j0.005 -j0.08 1.83 -112.24 0.48 100.03
-0.40-j0.10 j0.015 2.12 -127.56 2.31 199.48
The simulation results prove that the proposed FACTS device model in
various operating modes is capable of handling the scheduled real and reactive power
flows and bus voltage in indirect control mode. Operational and control constraints
are satisfied with a stable solution and an acceptable simulation time. It is shown that
51
3. STEADY-STATE MODELING A. Mete VURAL
well-known control functions, such as real and reactive power flow increase/decrease
as well as reversing real power flow are all implemented in this case study. Multi-
control objectives are met with the multi-converter FACTS devices in steady-state.
Table 3.8. Parameters of the GUPFC under different power flow control strategies
GUPFC
scheduled
system VSC1 output voltage VSC2 output voltage VSC3 output voltage
variables
P52ref + jQ52ref
magnitude phase angle magnitude phase angle magnitude phase angle
P54ref + jQ54ref
(kV) (º) (kV) (º) (kV) (º)
V5ref
-0.20+j0.10
0.50+j0.01 13.08 -40.10 0.74 42.53 0.59 67.02
1.04
0.40+j0.01
0.40-j0.01 12.80 -45.72 3.59 38.70 0.93 37.71
1.03
0.30-j0.01
0.65-j0.01 12.80 -47.02 3.67 40.23 1.71 35.26
1.03
-0.035-j0.20
0.08+j0.025 13.20 -38.63 1.22 89.46 1.29 207.44
1.065
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3. STEADY-STATE MODELING A. Mete VURAL
53
3. STEADY-STATE MODELING A. Mete VURAL
respectively with zero real power transfer between them. Qinjref max is
calculated according to operating constraints in Table 3.2 for Modes 1 and 2.
Numerical results are illustrated in Table 3.9.
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3. STEADY-STATE MODELING A. Mete VURAL
(a) Bus 1 voltage profile when real power transfer is from VSC1 to VSC4
(b) Bus 1 voltage profile when real power transfer is from VSC4 to VSC1
Figure 3.13. Comparative P-V curves of Bus 1
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3. STEADY-STATE MODELING A. Mete VURAL
(a) Bus 3 voltage profile when real power transfer is from VSC1 to VSC4
(b) Bus 3 voltage profile when real power transfer is from VSC4 to VSC1
Figure 3.14. Comparative P-V curves of Bus 3
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3. STEADY-STATE MODELING A. Mete VURAL
degree of freedom in power flow studies, changes real and reactive power flow
distributions on transmission lines, hence changes voltage profiles indirectly. This
situation should be considered for BtB-STATCOM design in practical applications.
3.5. Summary
A new modeling approach for power flow studies of the power systems
embedded with single- and multi-converter FACTS devices is presented in PSCAD
which is based on the regulation of magnitude and phase angle of the converters in
steady-state conditions. Operational and control constraints defined for each FACTS
device are solved in PSCAD using simple PI regulators. Direct and indirect control
modes for each FACTS device are tested and verified with various case studies in
different test systems. Graphical interface of PSCAD removes programming burden
such as coding or Jacobian matrix modification of NR method due to contributions of
shunt/series converters in terms of power injections. Also it contributes to a clear,
flexible, and understandable modeling approach but at the expense of PI regulator
tuning for each mode. The model is expandable so that the number of converters can
be increased with simple modifications to the constraints. Converter losses can be
explicitly defined and modeled. The proposed approach is also beneficial for large
scale systems if sufficient computing power and large memory are available.
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3. STEADY-STATE MODELING A. Mete VURAL
58
4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
4.1. Introduction
High power voltage source converter (VSC), developed from the applications
of low and medium power levels in industrial applications, is the building block of
the second generation FACTS devices having single or multiple converter
arrangements (Kazerani et al., 2002), (Tan et al., 2006). VSC can also be regarded as
a self-commutating converter, built from power semiconductors having turn-off
capabilities, such as GTO, GCT, or IGCT, and has the capability of both consuming
and generating reactive power which provides independent and simultaneous control
of real and reactive power flows. This property makes VSC superior when compared
with the line commutating converter which is only able to consume reactive power
from the power system and suffers from commutation failures of conventional
thyristors having only turn-on capabilities. VSC based topologies are generally
preferred over current source converters for FACTS applications at transmission
level due to higher losses and more complicated control (Hingorani et al., 2000),
(Kazerani et al., 2002), (Bahrman et al., 2003).
Converter-level modeling of the multi-converter FACTS devices requires
realistic high power VSC design for dynamic performance analysis and transient
stability studies if realistic time domain simulated responses are required to be
observed.
In converter design, the objective is to minimize switching frequency of the
power semiconductors hence minimize losses and to produce high quality quasi-
sinusoidal voltage waveform at transmission level with minimum or no filtering
requirements. Multi-pulse converter topology can be preferred over multi-level one
when back-to-back operation of two or more VSCs fed from a common DC link is
considered. Since DC link voltage control is easy due to a single DC voltage level as
opposed to multi-level structures for back-to-back VSCs in multi-converter FACTS
device applications (Soto et al., 2002), (Lee et al., 2003). On the other hand, quasi
multi-pulse topology can be preferred over true multi-pulse one due to: i) simple
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
modulation (PWM) control. There are different PWM methods in literature to reduce
harmonic content as much as possible to make AC output voltage resembling a pure
sinusoid. Unfortunately high frequency PWM control is considered uneconomical for
high power applications due to high switching losses, thus resulting both in
decreased conversion efficiency and in bulk cooling equipment.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
For the sake of clarity and to highlight basic operation, six-pulse VSC is
isolated from the three-phase system by turning on switches S1 and S3, and turning
off switch S2, shown in Figure 4.1. An external DC voltage source is connected at
the DC terminals and a three-phase resistive load RLD is connected at the AC
terminals. The circuit is simulated in PSCAD for 4 cycles with Vdc is set to 3.0 kV,
C=2000 µF, RLD and Rs is set to 1.0 MΩ and 0.001 Ω, respectively. GTO and diode
have turn on/off resistances of 0.005 Ω and 1.0E8 Ω, respectively. Snubber circuit
elements are ignored. The simulated phase-to-neutral and phase-to-phase voltage
waveforms of six-pulse VSC are shown in Figures 4.3 and 4.4, respectively. Each
phase is shifted by ± 120° with respect to other phases for balanced three-phase
operation. A simple square-wave switching scheme is applied with a switching
frequency of 50 Hz so that each GTO conducts only for 180° or 10 ms duration, as
shown in Figure 4.5. This type of switching is called 180-degree conduction in which
only three GTOs remain on at any time instant.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
the six- pulse operation in an analytical approach (Dávalos et al., 2005). The voltages
VBC and VCA exhibit similar patterns except phase shifts of -120° and +120°,
respectively.
∞
nπ
V AB (t ) = ∑ v n sin nwt + (4.1)
n =1 6
The peak value of nth voltage harmonic component is given in equation (4.2). Noting
that n=6r±1, (r=0,1,2,…). Even and triplen harmonics are zero.
4 nπ
vn = Vdc cos (4.2)
nπ 6
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
66
4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
voltage is √3 times the phase-to-neutral voltage, turns ratio of delta and wye
windings are selected such that the ratio of the secondary side of delta-winding to
that of wye-winding becomes √3.
∞
nπ
V AB (t ) = ∑ v n sin nwt + (4.3)
n =1 6
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
The peak value of nth voltage harmonic component is given in equation (4.4).
Noting that n=12r±1, (r=0,1,2,…).
8 nπ
vn = Vdc cos (4.4)
nπ 6
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
blocking voltage and peak current ratings, parallel and/or series combinations of
GTOs can also be employed for reasons of economy and easy availability of switches
with lower ratings (Sun et al., 2004). In this design, only one GTO with a reverse-
parallel diode per valve is utilized as the switching device to increase simulation
speed.
For the purpose of VSC control which will be discussed later, the overall
circuit is decomposed into two main parts, namely converters M and N, respectively.
Phase-A of twelve-pulse converter unit 1 is coupled to the phase-A of twelve-pulse
converter unit 2 with a single-phase transformer A1. Similarly, phase-B and phase-C
are coupled using transformers B1 and C1, respectively to make a quasi 24-pulse
converter (converter M). The second quasi 24-pulse converter (Converter N) is built
up using the other twelve-pulse converter units (3-4) and single-phase transformers
A2, B2, and C2. Phase-A of converter M and that of converter N are electro-
magnetically added using transformers A1 and A2, since the primaries are connected
in series. In a similar fashion, transformers B1 and B2 are used to sum phase-B of
converter M with that of converter N. Transformers C1 and C2 are used to sum
phase-C of converter M with that of converter N. Summing and interfacing
magnetics also couples VSC output voltage with the transmission level with no
requirement to an extra shunt coupling transformer by adjusting the voltage ratings
of primaries of A1, A2, B1, B2, C1, C2.
Phase shift angle between two adjacent twelve-pulse converters should be
7.5° (Singh et al., 2009). So, 7.5º, 0.0º, -7.5º, and -15º phase shifts are applied to the
gating signals of each upper six-pulse converter of twelve-pulse unit 1,3,2,4,
correspondingly. This arrangement also satisfies that twelve pulse units 1 and 3 and
units 2 and 4 can operate as two independent quasi 24-pulse converters, respectively.
On the other hand, gating signals of each lower six-pulse converter of four twelve-
pulse units are shifted by 30° one by one with respect to each upper side VSC for
proper twelve-pulse operation. Figure 4.11 shows only ¼ of the PSCAD
implementation of the quasi multi-pulse VSC, which is designed using PSCAD
master library components. Figure 4.12 shows PSCAD implementation of two
different magnetic interfaces required for quasi multi-pulse operation.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
More specifically, Figure 4.12a illustrates the details of the magnetic interface
for twelve-pulse operation, which is modeled as a PSCAD default module. Summing
and magnetic interface for quasi multi-pulse VSC is presented in Figure 4.12b, which
is modeled directly on the main project page of PSCAD.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
series coupling magnetic interface shown in Figure 4.13 can be designed to directly
inject three-phase AC voltages of the series VSCs to three-phase transmission line.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
parameter for six-pulse operation and hence quasi multi-pulse VSC, regardless of the
FACTS device and the multi-pulse configuration is the phase shift applied to the gate
pulse pattern of the GTOs. In order to bring an extra control degree, the “2-angle
control” method is adopted from literature (Hagiwara et al., 2003). In this approach,
quasi multi-pulse VSC can be controlled both in magnitude and phase angle by
appropriate two kinds of phase shifts even GTOs are switched at line frequency. The
calculation procedure of these two shift angles are given in the next section.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
r
VM = VM ∠φ M = V M ∠(α − δ )°
r (4.5)
V N = V N ∠φ N = V N ∠ − (α + δ )°
−1
VQ ref
δ = tan (4.6)
VD ref
phM = θ S + (α − δ )
phN = θ S − (α + δ ) (4.7)
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
48r±1 (r=1,2,3,…) almost obtained by true 48-pulse configuration (Lee et al., 2003),
(Geethalakshmi et al., 2007).
∞
V AB (t ) = ∑ v n sin (nwt + 18.75°n + 11.25°i ) (4.8)
n =1
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
The peak value of nth voltage harmonic component is given in equation (4.9). Noting
that n=48r±1, (r=0,1,2,…) and i= -1 for n=47,95,… and i=1 for n=49,97,…,
respectively.
32 nπ
vn = Vdc cos (4.9)
nπ 6
Although theoretically possible, the converter topology can become more and
more complicated if the pulse numbers above 48 are applied that can be rarely
justified in practical applications. It is shown that a quasi 48-pulse VSC is sufficient
for 100 MVA STATCOM application (Schauder et al., 1995) and a true 48-pulse
topology is designed for 80 MVA SVC (Mori et al., 1993).
The proposed quasi multi-pulse VSC is designed such that the AC outputs of
two quasi 24-pulse converters are magnetically added, each of which is
independently and externally phase shift controlled. On the other hand, four twelve-
pulse converter units are designed together with appropriate phase shifts to operate as
quasi 48-pulse converter if external phase shifts are set to zero. In this sense, at the
best case, the proposed VSC can show the harmonic performance of quasi 48-pulse
topology and thereby named as “quasi multi-pulse”. In Chapters 5 and 6, the actual
THD content of the proposed quasi multi-pulse VSC will be evaluated and compared
with the IEEE standards when its shunt/series combinations are utilized in GUPFC,
IPFC, and BtB-STATCOM configurations.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
control requires the calculation of VDref and VQref from external control loops for each
VSC of the multi-converter FACTS device. This situation is thoroughly studied and
discussed in detail in Chapters 5 and 6. In the verification procedure, at first the
output of the quasi multi-pulse VSC is forced to align on four different quadrants on
the graph of polar plot, as shown in Figure 4.19. This case study shows how the
phase angle of VX can be controlled in the range between 0° and 360°. Secondly, it is
demonstrated how both the magnitude and phase angle of the output of quasi multi-
pulse VSC can be freely controlled using randomly selected simulation results under
the condition that the output of each quasi 24-pulse converter is fixed and equal to
7.75 kV. The cases are shown in Figure 4.20.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
ΦM (ref)=0.0°
ΦN (ref)=0.0°
D D D
7.75677 -0.1203 7.75677 -0.1203 15.5135 -0.1203
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
VX in
first quadrant
ΦM (ref)=90.0°
ΦN (ref)=0.0°
D D D
7.74924 90.04 7.7533 0.01782 10.9686 45.03
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
VX in
second quadrant
ΦM (ref)=180.0°
ΦN (ref)=90.0°
D D D
7.75677 179.9 7.74439 90.18 10.9589 135.1
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
VX in
third quadrant
ΦM (ref)=270.0°
ΦN (ref)=180.0°
D D D
7.74925 -89.97 7.7533 -180 10.9686 -135.2
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
VX in
fourth quadrant
ΦM (ref)=0.0°
ΦN (ref)=270.0°
D D D
7.7533 0.0736 7.74925 -90.12 10.9553 -44.95
(kV) (°) (kV) (°) (kV) (°)
Figure 4.19. Four quadrant operation of the proposed quasi multi-pulse VSC
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
ΦM (ref)=30.0°
ΦN (ref)=60.0°
D D D
7.75497 30.02 7.74879 59.89 14.9759 44.94
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
ΦM (ref)=174.0°
ΦN (ref)=320.0°
D D D
7.74935 174 7.75164 -40.17 4.61606 -113.9
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
ΦM (ref)=190.0°
ΦN (ref)=350.0°
D D D
7.75272 -169.9 7.75164 -10.12 2.86963 -91.23
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
ΦM (ref)=250.0°
ΦN (ref)=12.0°
D D D
7.75174 -110 7.75243 12.02 7.54778 -49.05
(kV) (°) (kV) (°) (kV) (°)
Voltage VM Voltage VN Voltage VX
ΦM (ref)=180.0°
ΦN (ref)=0.0°
D D D
7.75331 -180 7.75331 0.01782 8.75729e-... 0
(kV) (°) (kV) (°) (kV) (°)
Figure 4.20. Flexible magnitude/phase angle controlled quasi multi-pulse VSC
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
4.5. Summary
A realistic and high power quasi multi-pulse VSC for multi-converter FACTS
devices is proposed and designed with given all details down to the GTO level,
including magnetic interface and control scheme. First, working principles of
elementary two-level six-pulse and twelve-pulse converter topologies are discussed.
Later on, quasi multi-pulse VSC is designed using four twelve-pulse converter units
which is more accurate than existing low-order or average models. Line frequency
switching scheme is applied to minimize converter losses and voltage/current
stresses on each GTO valve are fairly decreased using multi-converter structure. 2-
angle control method is adapted from literature to gain an extra control degree to the
proposed VSC without changing the magnitude of the DC link voltage. Harmonic
content is quantitatively evaluated in terms of individual harmonic voltages and
THD. Power and voltage rating are flexible so that quasi multi-pulse VSC can be
simulated with regard to different operating requirements. For the next two chapters,
the designed quasi multi-pulse converter topology will be used as the building
element for GUPFC, IPFC, and BtB-STATCOM where the test and the verification
of the model will be done digitally in PSCAD in one sense.
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4. VOLTAGE SOURCE CONVERTER DESIGN A. Mete VURAL
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5. DYNAMIC MODELING STUDIES A. Mete VURAL
5.1. Introduction
85
5. DYNAMIC MODELING STUDIES A. Mete VURAL
2010), with only bus voltage control (Bharathi et al., 2011). IPFC based on multi-
output sparse matrix converter switching at relatively high frequency of 10 kHz is
modeled (Hosseini et al., 2011).
Dynamic modeling studies of GUPFC are rather limited in literature when
compared with IPFC based studies although there are plenty of UPFC based dynamic
studies. For instance, average converter models are used for each VSC of GUPFC
(Lubis 2011a). Alternatively in average modeling approach, the controlled voltage
source representing each VSC of GUPFC is embedded into the power system model
directly and the simulation engine iteratively solves the system equations (Fardanesh
et al., 2000), (Sun et al., 2003).
Converter-level modeling studies of GUPFC have recently been published.
Elementary two-level six-pulse converter topology is the most common power circuit
scheme (Prakash et al., 2007), (Sujin et al., 2012), (Abdul et al., 2012). Sixty-pulse
converter model of GUPFC comprised of five three-phase three-level converters and
five phase-shifting transformers are presented (Lubis 2011b).
Dynamic modeling of BtB-STATCOM is approximated using average
modeling approach where each output of VSC is modeled as controllable ideal
voltage source (Tyagi et al., 2006), (Xinghao et al., 2009), (Lee et al., 2011),
(Parkhideh et al., 2009). On the other hand, converter-level models of BtB-
STATCOM are more detailed. For instance, two elementary two-level six-pulse
converters are used in BtB-STATCOM configuration (Ruihua et al., 2005), (Jovcic et
al., 2007), (Liu et al., 2010). Converter structure is pretty simple that does not reflect
realistic BtB-STATCOM operation completely. More detailed converter topologies
are alternatively considered. For instance quasi multi-pulse converter topology
consisting of sixteen six-pulse units are combined to build each VSC of BtB-
STATCOM (Hagiwara et al., 2003). The BtB system consists of two sets of four
three-phase neutral-point-clamped converter units each having twelve GTOs driven
by PWM (Hagiwara et al., 2005), (Hagiwara et al., 2008). 24-pulse three-level
voltage source converters with fundamental frequency switching for HVDC system
is proposed (Madhan Mohan, et al., 2009).
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Due to nonlinear nature of converter switching and the interactions among the
controllers of the multi-converter FACTS device, finding optimum parameters of the
control scheme while satisfying stable operation of the multi-converter FACTS
device is not an easy task. It is presented that the inherent dynamic interactions
between individual controllers of the UPFC can lead to unstable operation even
though each controller of UPFC itself is designed satisfactorily (Wang et al., 2000).
For a GUPFC, the situation can become desperately as more control functions are
attributed to GUPFC. One solution depends on analytical approaches such as ziegler-
nichols oscillation method, smith predictor, and pole assignment methods, which
require exact mathematical model of the system which is difficult to obtain without
simplification or averaging (Goodwin et al., 2000). Another solution may suffer from
the long computing time to find the optimum parameters where several simulation
runs exist to select the best parameters (PSCAD, 2005). Alternatively, a direct search
algorithm, which is called “simplex method”, is used in this research (Neider et al.,
1965) that is integrated into the PSCAD (Gole et al., 2005). This method does not
rely on gradient information and applicable for highly-nonlinear multi-input multi-
output systems without obtaining mathematical models and hence suitable for
finding the minimum of an objective or a cost function defined by several variables.
In this research, simplex method is executed not only to find the optimum multi-
controller parameters but also to find the best parameters for a specific designed
component in PSCAD.
Simplex is the name of a geometric figure whose vertices are defined by
variable numbers. For example, for two-variable optimization, simplex is a triangle,
for three-variable optimization, simplex is a tetrahedron. The problem becomes a
pattern search that compares function values at all vertices. The worst vertex, where
the cost function is the largest, is rejected and replaced by a new vertex. A new
simplex is formed until the function values at the vertices are the smallest. Simplex
size is then reduced iteratively and the coordinates of the minimum point are found.
The flow chart of the simplex optimization method is shown in Figure 5.1.
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Update No Execute
parameter set Convergence simplex algorithm
?
Yes
Output
End
parameter set in a
file
Figure 5.1. Flow chart of the simplex optimization method in PSCAD
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shunt VSC. For series VSC, the rating is modified as 36/36 kV, j0.025 pu. Each
single-phase transformer of series coupling magnetic interface is rated at 60 Hz,
33.33 MVA, 104.13/40 kV, j0.01 pu.
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determine the required axis components of shunt and series converter voltages. The
control loops are designed according to the fact that the quadrature component (q-
axis) of the series injected voltage mainly controls real power flow, while the direct
component (d-axis) of the series injected voltage controls reactive power flow (Ye et
al., 2006), (Mishra, 2006), (Liming et al., 2007), (Xia et al., 2010). Since GUPFC’s
losses are met by VSC1, the shunt converter control is the DC link voltage control, E
and the voltage magnitude control of Bus 4, V4, achieved by VshD (Figure 5.3a) and
VshQ (Figure 5.3b), respectively. On the other hand, series VSC2 controls real and
reactive power flows of Line L-45, achieved by Vse2Q (Figure 5.3c) and Vse2D (Figure
5.3d), respectively. Series VSC3 controls real and reactive power flows of Line L-46,
achieved by Vse3Q (Figure 5.3e) and Vse3D (Figure 5.3f), respectively. A total of
twelve parameters of GUPFC’s control scheme (6xproportional gain, Kp and
6xintegration time constant τi) is optimized using simplex method to alleviate
controller interaction.
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{
p = K p1 , τ i1 , K p 2 , τ i 2 , K p 3 , τ i 3, K p 4 , τ i 4 , K p 5 , τ i 5 , K p 6 , τ i 6 } (5.1)
(
T
F ( p ) = ∫ (V 4 ref − V 4 ) 2 + ( E ref − E ) 2 + (Q 45 − Q45 ) 2 + ...
ref
t =0
... + ( P45 ref − P45 ) 2 + (Q46 ref − Q46 ) 2 + ( P46 ref − P46 ) 2 dt ) (5.2)
The total simulation time T in equation (5.2) is chosen much longer than the
settling time of the whole control system. Reference values of real and reactive
power flows are chosen same as in case 1 in the next section. F(p) is plotted against
iteration number in Figure 5.5 and the optimum parameters are listed in Table 5.1.
The algorithm is converged in 504 iterations for a tolerance of 1.0E-6. Due to
interaction between converters, the individual converter design is not preferred and
only one cost function is identified to obtain stable and reasonably dynamic
performance.
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and under two types of faults. The simplex optimized controller parameters listed in
Table 5.1 are used in the simulations and the nominal DC link voltage of the GUPFC
is controlled at 2.0 kV throughout all simulation cases. Solution time-step is set to
100 µs in PSCAD.
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(g) Phase shifts for converters M and N of VSC1 (ΦM and ΦN) during start-up
(h) Phase shifts for converters M and N of VSC2 (ΦM and ΦN) during start-up
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(i) Phase shifts for converters M and N of VSC3 (ΦM and ΦN) during start-up
Real power flow references for both lines (L-45, L-46) are decreased from 1.0
pu to 0.85 pu and from 0.74 pu to 0.60 pu at 10.5 s, simultaneously. The other
references of GUPFC control loops are kept unchanged as in case 1. Figures 5.7a-f
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show the traces of real and reactive power flows of Line L-45 and L-46, GUPFC DC
link voltage, and V4, respectively. Real power traces reach to their reference values
within about 0.5 s after the step change command is applied with no steady-state
error. The transmission line reactive power flows stay constant as zero after
following a 6 % undershoot and 10 % overshoot in Q45 and Q46, respectively. PI
controller could keep GUPFC DC link voltage in its reference so that the trace has
almost no change towards step change command to real power flows. The response
of V4 after the step change command in real power flow references is almost constant
on 1.0 pu line. PI control scheme for each control loop in this case study exhibits
stable performance.
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In this case, at 10.5 s, reactive power flow references for Line L-45 and L-46
are changed from 0.0 pu to -0.15 pu and from 0.0 pu to -0.10 pu, simultaneously. The
other references in GUPFC control loops are kept constant as in case 1. Figures 5.8a-
f show the traces of real and reactive power flows of Line L-45 and L-46, GUPFC
DC link voltage, and V4, respectively. When comparing cases 2 and 3 by examining
Figures 5.7a and 5.8b, the settling time of the reactive power control loop is about
0.5 s longer than that of real power control loop. The same amount of delay in the
response of reactive power control loop in Figure 5.7c is also observed when
compared with the response of real power control loop in Figure 5.8d. The real
power flow controllers response to the step change command of reactive power flows
with a 7% and 2.6 % overshoot, respectively. After following these transients,
GUPFC could bring real and reactive power flows to their desired values with no
steady-state error. GUPFC DC link voltage is controlled tightly so that the trace has
almost no change towards step change command to reactive power flows. When
comparing Figures 5.7f and 5.8f, the response of V4 after the step change in reactive
power flow reference is more ludic than the case after the step change in real power
flow reference. The sluggish response of GUPFC is due to the fact that voltage
magnitude is sensitive to reactive power.
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(b) Reactive power flow control of Line L-45 for a step-change at 10.5 s
(d) Reactive power flow control of Line L-46 for a step-change at 10.5 s
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Figures 5.9g-l also show the simulated voltage and current waveforms of the GUPFC
converters under single-phase to ground fault condition.
(a) Line L-45 real power flow response to phase-A to ground fault at 10.5 s
(b) Line L-45 reactive power flow response to phase-A to ground fault at 10.5 s
(c) Line L-46 real power flow response to phase-A to ground fault at 10.5 s
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(d) Line L-46 reactive power flow response to phase-A to ground fault at 10.5 s
(e) Bus 4 line-to-line rms voltage response to phase-A to ground fault at 10.5 s
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(a) Line L-45 real power flow response to three-phase short circuit at 10.5 s
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(b) Line L-45 reactive power flow response to three-phase short circuit at 10.5 s
(c) Line L-46 real power flow response to three-phase short circuit at 10.5 s
(d) Line L-46 reactive power flow response to three-phase short circuit at 10.5 s
(e) Bus 4 line-to-line rms voltage response to three-phase short circuit at 10.5 s
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Table 5.2 lists the average recorded THD values of the voltages measured
from three common coupling points (Buses 4-5-6) between GUPFC and the power
system when GUPFC is commanded to control real and reactive power flows of lines
L-45 and L-46 with the reference values given in case 1. Records of the simulation
run lasting for 12.5 s show that GUPFC switching at fundamental frequency of 60 Hz
does not cause the violation of the THD upper limit for 230 kV transmission level
(IEEE, 1993). It is seen that voltage distortions at common coupling points are within
the acceptable limits. Consequently, filtering is not required even GTOs are
switching at fundamental system frequency.
5.3.5. Discussion
GUPFC is built using two series and one shunt quasi multi-pulse VSC
designed in Chapter 4. GUPFC dynamic performance on the control of real and
reactive power flows of two neighboring transmission lines and bus voltage control
is evaluated through different simulation scenarios including faults on WSCC 3-
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The dynamic performance of IPFC suffers from the strong dynamic interaction
between real and reactive power flows due to inherent properties of AC power
transmission. To reduce or eliminate this coupling effect, a number of studies on other
members of FACTS devices are available in literature. It is realized that these studies
rely on decoupling parameters of approximated FACTS device model or converter-
level model of elementary six-pulse VSCs driven by high frequency PWM methods,
which is not realistic for high power applications. Firstly, a d-q current controller is
proposed with no-cross coupling for a grid connected inverter (Schauder, 1991). Later
on a new control scheme originated from this controller in which a decoupled
controller with an internal predictive loop for UPFC is suggested (Papic et al., 1997).
In the proposed control scheme, the parameters of reactance of series coupling
transformer and system bandwidth are required for gain design. Other articles propose
different types of decoupled controllers for non-converter-level model of UPFC where
an equivalent ideal voltage source model of UPFC is considered with no harmonics
(Yu et al., 1996), (Yam et al., 2002), (Papic et al., 2003), (Ye et al., 2006), (Farahani et
al., 2006), (Ande et al., 2007), (Ma, 2007). A decoupling controller is designed, but
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control performance counts on exact system parameters and UPFC model (Yu et al.,
1996). A dynamic decoupled compensator for UPFC is designed (Yam et al., 2002).
The design relies on classical control design techniques which rely on exact
mathematical model of the system, damping ratio and system bandwidth should also
be exactly known. A decoupling matrix compensator consisting of four controllers is
developed that relies on ABCD parameters of approximated UPFC model (Farahani et
al., 2006). A decoupled UPFC controller for dynamic control of real and reactive
power flows is considered (Ande et al., 2007). UPFC is experimentally validated by
six-pulse VSCs where PWM control is used (Liming et al., 2005). To achieve
decoupling, reactance values of shunt and series coupling transformers should be
exactly known.
In this research, the decoupling effect between real and reactive power flow
control loops is reduced by a new hybrid fuzzy PI (HFPI) control scheme applied to
IPFC. The proposed controller is based on conventional simplex optimized PI
controller operating in conjunction with Mamdani-type fuzzy inference system with
linearly distributed linguistic rules. With this way, a fast response is obtained with
minimal interaction to track the changes in reference values of the real and reactive
power flows. Design phase neither requires exact mathematical description nor system
transfer function. The performance of the proposed HFPI controller is compared with
both conventional PI control and PI control with analytically computed feed-forward
decoupled gains.
Assuming series resistance and inductance of tr1 in Figure 5.11 are included
into the transmission line parameters RL and XL, respectively. Then, the current on
Line-1, IL can be derived as
VS − V R − V X
IL = (5.3)
R L + jX L
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where symbol (*) denotes complex conjugate and PS and QS denote sending-end real
and reactive power flows on Line-1, respectively. Assuming VR leads VS by a small
angle δ (cos δ≈1, sinδ≈0), PS and QS can be expressed as
Ps RL 2 + X L 2 VQ RL Qs − Qs 0 Ps 0
Q = A − V + X − P + P + Q (5.5)
s X L2 D L s s0 s0
d PS RL 2 + X L 2 d VQ RL d QS
Q = +
dt − VD X L dt
A − P (5.6)
dt S X L2 S
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1 R
VQ ref = K p1 ( PS ref − PS ) + ∫ ( PS ref − PS )dt − L Q S
Ti1 XL
1 R
− VD ref = K p 2 (QS ref − QS ) + ∫ (QS ref − QS )dt + L PS (5.8)
Ti 2 XL
where VQref and VDref denote desired d-q components of series converter voltage. PS
and QS are respectively the current values of real and reactive power flows measured at
time t. Kp1 and Kp2 are the proportional gains of real and reactive power flow
controllers, respectively. Ti1 and Ti2 are the integration time constants of real and
reactive power flow controllers, respectively. In this case, the control scheme
mentioned so far is regarded as PI control with decoupled gains (PI+DG). PSCAD
implementation of PI+DG control scheme is shown in Figure 5.12. Noting that if RL/XL
ratios are set to zero or port A of sum blocks are disabled then the control scheme
simply becomes PI control.
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The system response is examined for sequences of set-point changes when only
PI controllers with optimum parameters are employed. For example, if QS hugely
deviates from its set-point while PSref is decreased sharply, a large control signal ΔVD
that pulls it toward to its set-point is expected. Similarly, when QSref is suddenly
increased, PS tends to decrease and a large control signal ΔVQ is required. As a first
step, x(k) is defined as the input set of crisp numerical signals of Pe, ΔPe, Qe, ΔQe at
sampling instant k, limited to its universe of discourse. Pe and Qe are the real and
reactive power flow errors, ΔPe and ΔQe are the real and reactive power flow error
rates, respectively. x(k) is then fuzzified according to seven linguistic characteristics,
defined for its each element. Abbreviations in Figure 5.16 for the membership
functions (MFs) that quantify the meaning of linguistic characteristics are the
following: N3: big negative, N2: medium negative, N1: small negative, Z: zero, P1:
small positive, P2: medium positive, and P3: big positive. Intersection point M is
specific for each member in x(k).
Output set y(k) also needs fuzzification at the sampling instant k using
membership function (MF) set for ΔVQ and ΔVD depicted in Figure 5.17. Intersection
point N is specific for each member in y(k).
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Rule base for output ΔVQ is listed in Table 5.3 which is identical to that of ΔVD,
but designed for ΔQe/Qe. Every entity merges the error rate and the error fuzzy set
values. For instance, first rule is
In the next step, the min fuzzy operator is applied as the antecedent of the rule,
which has more than one part that should be ANDed with each other. The min fuzzy
operator is also used in the implication step, implemented for each rule. Here, the
output fuzzy set is truncated by a real number given by the antecedent of the rule. The
result of implication is innately fuzzy, so to determine crisp outputs (ΔVQ, ΔVD), the
popular centroid defuzzification scheme is utilized as the last step. Finally, the actual
outputs of FUDE are obtained. For instance, ΔVQ at the sampling instant k can be
written using equation (5.9). µ(i) and bi are the aforementioned MF and the center of
MF of the consequent of rule i, respectively. The control surfaces of the proposed
FUDE are shown in Figure 5.18.
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∑i49=1 bi ∫ µ (i )
∆VQ (k ) = 49
(5.9)
∑ ∫ µ (i )
i =1
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Simplex method iteratively finds the optimal parameter set p={Kp1, Kp2, Ti1,
Ti2} for PI controllers of the master VSC and the slave VSC by minimizing the cost
functions given in equations (5.10) and (5.11) depending on sum of ISEs of the
controlled variables. PSCAD implementation of simplex method is shown in Figure
5.21.
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( )
T
F ( p ) = 100 ∫ ( P2 ref − P2 )2 + (Q2 ref − Q2 )2 dt (5.10)
t =0
( )
T
H ( p ) = 100 ∫ ( P1ref − P1 ) 2 + ( E ref − E ) 2 dt (5.11)
t =0
T is total simulation time in equations (5.10) and (5.11). While FUDE is off,
simplex method is executed for a sequence of unit step changes applied to P2ref and
Q2ref for Line-2, which are same as in case 1 in the next section. During optimization
routine, the variations of F(p) and H(p) against iteration number are plotted in Figures
5.22a and 5.22b, respectively.
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Optimum parameter set is listed in Table 5.4. First, parameters of the master
control scheme are optimized using equation (5.10) under the condition that slave
controller is employed with pre-defined parameters providing a robust and stable IPFC
performance. Here it is not ensured that these parameters are optimal, but they give
satisfactory dynamic performance. Secondly, parameters of slave control scheme are
optimized using equation (5.11) while the solution of the first case results is applied to
master control scheme. The algorithm is executed for a tolerance of 1.0E-6.
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5.4.4.1. Case 1
In this case study, IPFC is activated by opening the switches (sw1, sw2) and
the dynamic performances of aforementioned controllers are simulated and compared
when the system is subjected to a sequence of unit-step changes in real and reactive
power flow commands of Line-2. Reference for real power flow on Line-1 is set as 2.3
pu and IPFC DC link voltage is regulated at 1.0 kV throughout the case study. As
observed in Figure 5.23, reactive power flow command is altered to force coupling
during the instants when real power flow command is constant. Although PI controller
is parameter optimized, relatively large fluctuations in real power flow are observed at
times, t=1.0 s, 2.0 s, and 3.0 s, respectively (Figures 5.23a-c).
PI controller with decoupled gains (PI+DG) gives better results when the
dynamic performance is compared with that of PI controller only. Although PI
controller or PI+DG gives satisfactory steady-state tracking performance, inherent
coupling between power flow control loops are not avoided and IPFC dynamic
performance is adversely affected. On the other hand, HFPI controller has the superior
decoupling feature as evidence from the response curves since the variations in real
power flow is effectively minimized when reactive power flow command is changed.
Moreover, Figures 5.23d-f gives a comparison between the responses of
different controllers to step-changes in real power flow command. HFPI controller
responses with less oscillations and shows reduced overshoot characteristics. The
dynamic performance of reactive power flow control loop with different control
schemes are also evaluated in this case study.
Figure 5.24 shows the traces of different reactive power flow controllers in
response to unit-step change in real power flow command. As shown in Figures 5.24a-
c, HFPI controller performance is superior to either PI controller or PI+DG on tracking
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reference signal and HFPI controller effectively minimizes the coupling effect between
two power flow control loops.
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with PI+DG. DC link voltage excursions of IPFC for different control schemes are
depicted in Figure 5.26. DC voltage controller is almost robust and gives satisfactory
response for all control modes. But when the comparisons are particularly made at
instants (t=1.0 s, 1.5 s, 2.0 s, 2.5 s, 3.0 s, 3.5 s), relatively smaller spikes are observed
at the simulated waveforms in case of HFPI controller. Figure 5.27 compares the d-q
components of injected current of the master converter in case of three controllers.
Prominent time instants are marked with red rectangles when real power flow
reference is changed in case of iD and when reactive power flow reference is changed
in case of iQ. These spikes in marked regions showing the interactions between the two
power flow controllers are effectively reduced by the proposed HFPI controller.
Although the spikes caused by HFPI controller are practically the same when
compared with the ones caused by PI controller, HFPI controller weakens the spikes
much better than PI+DG. Figure 5.28 shows control signals (VDref and VQref) for inner
control loop and the measured voltages (VD and VQ) of the master converter at the
primary windings of series coupling transformer Tr1. It is ensured that the “2-angle
control” block operates stable and the orthogonal components of the master converter
voltage perfectly trace their pertinent reference values in case of HFPI controller.
Figure 5.29 depicts anode-to-cathode voltage of one selected GTO from Group M of
the master converter in case HFPI controller is activated. As designed for quasi multi-
pulse operation, GTO is triggered only once in one fundamental cycle of 50 Hz.
5.4.4.2. Case 2
In this case study, controller references are kept exactly the same as in case 1
and RL/XL ratio of the Line-2 is increased by three times to investigate and compare
the parameter sensitivity of the three control schemes. Figures 5.30 and 5.31 show
comparative tracking performances of the controllers for real and reactive power
flows of the Line-2, respectively. ISE and IAE performance indices are listed in
Table 5.5 for 0.9 s ≤ t ≤ 5.0 s. As shown in Figures 5.30a-c, real power flow control
loop is interacted adversely with reactive power flow control loop when PI+DG is
employed.
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Figure 5.25. Dynamic performance of real power flow controller for slave VSC
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PI+DG has the maximum overshoot of all controllers and gives relatively the
slowest response when compared with the other control schemes. The same situation
is also observed in Figures 5.31a-c when reactive power flow of Line-2 is controlled
by PI+DG during set-point changes in real power flow. As expected, the
performance of PI+DG for both real and reactive power flow control loops degrades
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significantly, since decoupled gains are designed offline using transmission line data.
When comparing cases 1 and 2 quantitatively, an increase of 32.68% in ISE and an
increase of 80% in IAE are observed for real power PI+DG controller. Similarly, an
increase of 62.55% in ISE and an increase of 127.18% in IAE are observed for
reactive power PI+DG controller. It is because of the PI gains are optimized for the
operating conditions in case 1 that the dynamic performance of PI controller
slightingly weakens when compared with that of case 1.
Even though the system parameters are changed, HFPI controller successfully
reduces the interactions between real and reactive power flows with the lowest ISE
and IAE indices when compared with either PI controller or PI+DG. Furthermore, it
is observed in Figure 5.30d-f and in Figure 5.31d-f that HFPI controller gives a
smooth response and greatly improves rise time and settling time of the control loops
when responding to set-point changes.
Table 5.6 lists the highest THD values computed using the first 63 harmonics
at four common coupling points between IPFC and the power system. Records for
1.0 s≤t≤5.0 s confirm that IPFC does not cause the violation of the THD upper limit
of 2.5 % for 154 kV transmission level (IEEE, 1993). Consequently, filtering is not
required even GTOs are switched at fundamental frequency.
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5.4.5. Discussion
The proposed HFPI controller minimizes the interactions between the control
loops of real and reactive power flows and gives a smoother response when
compared with either PI+DG or PI controller. Even system coefficients change, it is
still able to alleviate these interactions and robust to uncertainty. On the other hand,
the performance of PI+DG strongly relies on the knowledge of system parameters
and only performs better than PI controller under the condition that the model
parameters match with the parameters of decoupled gain design. HFPI controller
does not disturb other IPFC control loops, such as power flow control on Line-1 and
DC link voltage control although it introduces small voltage ripples in the DC
interface. So the interactions between the controllers are obtained minimum for
multi-functioning FACTS device which is highly desired.
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VSC2 control is the real power transfer among the two VSCs through the DC
link and voltage magnitude control of Bus 3, V3, achieved by Vsh2D (Figure 5.32c)
Vsh2Q (Figure 5.32d), respectively. The chosen PI parameters for VSC1 and those of
VSC2 of BtB-STATCOM are given in Appendix C.
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(e) Phase shifts for converters M and N of VSC1 (ΦM and ΦN) during start-up
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(f) Phase shifts for converters M and N of VSC2 (ΦM and ΦN) during start-up
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(c) Phase shifts for converters M and N of VSC1 (ΦM and ΦN)
(d) Phase shifts for converters M and N of VSC2 (ΦM and ΦN)
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(e) Phase shifts for converters M and N of VSC1 (ΦM and ΦN)
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(f) Phase shifts for converters M and N of VSC2 (ΦM and ΦN)
(g) VSC1 controller output signals in response to phase-A to ground fault at 10.5 s
(h) VSC2 controller output signals in response to phase-A to ground fault at 10.5 s
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5.5.4. Discussion
5.6. Summary
In this chapter, quasi multi-pulse VSC is adapted for the three-types of multi-
converter FACTS devices. Power circuit, gating pulse generation circuits, and 2-
angle control method for the quasi multi-pulse VSC, mentioned in Chapter 4, are also
verified for different control actions together with different disturbance scenarios in
one sense. If no further performance is required in terms of power quality, eight six-
pulse converters operating together for VSC configuration can be used without the
need for any AC filters, since measured THD levels always lie below IEEE-519
standard. Independent control of voltage magnitude and phase angle of the
converters without high frequency PWM methods makes use of separate control
functions for real and reactive power possible. Although the concerned FACTS
devices have many possible operating modes, it is anticipated that the shunt
converter is operated in automatic voltage-control mode (GUPFC, BtB-STATCOM)
and the series converter (GUPFC, IPFC) is operated in automatic power-flow control
mode. The bottleneck of finding a lot of suitable parameters for many controllers that
should operate together in stable and robust is overcome by simultaneously tuning of
these parameters using simplex method. This solution is practically applied for the
controllers of GUPFC and IPFC when different cost functions are defined. A novel
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5. DYNAMIC MODELING STUDIES A. Mete VURAL
HFPI controller for IPFC is designed to decouple the control loops of real and
reactive power flows that can be generalized to any series converter of the multi-
converter FACTS device. The simulation results prove superior dynamic
performance when compared with the simplex optimized PI controller both
without/with analytically computed feed-forward decoupling gains.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
6.1. Introduction
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behavior of DFIG is similar to SEDCIG when the crowbar system of the DFIG
protects the converter under grid fault by bypassing the rotor circuit over the crowbar
impedance.
Combining two completely different machine stability concerns mentioned
above, stability of the power systems connected with the wind farm is enhanced by
GUPFC, with the following simultaneous control tasks which are proposed for the
first time: i) oscillation damping of wind farm integrated power system by a self-
tuning fuzzy damping controller (STFDC), ii) multi-line real and reactive power flow
control, iii) AC bus voltage control.
STFDC proposed in this chapter is further adapted for IPFC for damping
inter-area mode of oscillations of a power system consisting of several conventional
synchronous generators. Finally, the performances of the PI controllers proposed for
BtB-STATCOM in the last chapter is investigated in terms of oscillation damping
and hence to improve transient stability of the power systems in this chapter.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
2011). On the other hand, IPFC is fuzzy and/or neural network controlled to improve
stability based on average modeling approach (Mishra et al., 2002), (Parimi et al.,
2010a), (Belwanshi et al., 2011), (Banaei et al., 2011). Different from those, transient
stability of a multi-machine system is improved by IPFC using derived energy
function for IPFC which is developed from an average model (Azbe et al., 2009).
Three-phase model of IPFC is derived using switching functions for a twelve-pulse
VSC based IPFC for SSR studies (Padiyar et al., 2007).
A non-linear control scheme for BtB-STATCOM is developed using an
average modeling approach (Lee et al., 2011). The stability studies are conducted on
Phillips-Heffron model of SMIB system which includes the average model of two
BtB VSCs (Banaei et al., 2009b). A supplementary control for VSC based BtB link
in damping SSR of series capacitive compensated transmission system is studied
using an average model of each VSC (Faried et al., 2009).
According to literature review results, transient stability studies of GUPFC,
IPFC, and BtB-STATCOM generally rely on average models included into Phillips-
Heffron SMIB system or multi-machine systems, rather than using converter-level
models. This chapter is aimed to investigate these FACTS devices on transient
stability enhancement using converter-level modeling approach, together with a
novel damping control scheme.
The wind can be modeled with the following equation that properly includes
spatial effects of the wind behavior such as gusting, ramp changes, and background
noise (Anderson et al., 1983),
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where VW is the wind speed, VWB is the base or mean wind speed which is always
assumed to be present where the wind generator is required to be in service. VWG is
the gust wind component, VWR is the ramp wind component, and VWN is the noise
wind component. In this chapter, only transient fault simulations are considered
where the simulated events last up to only 12.5 s. Moreover, the wind farm
considered here is aggregations of many single wind turbines in which wind speed
variations can cancel each other (Sorensen et al., 2002), (Jauch et al., 2007), (Erlich
et al., 2007). That’s why natural wind variations (VWG,VWR,VWN) are not taken into
account. VWB is set to 14 m/s allowing all turbines to produce rated power (Jauch et
al., 2007), (Kusiak et al., 2010).
The mechanical system mainly consists of blade and shaft which transforms
wind kinetic energy into rotational motion. Shaft dynamics are not presented in this
research which is characterized by blade speed, hub speed, gear box speed, and the
generator mechanical speed (Anderson et al., 1983). The available wind power is
assumed to be captured by horizontal axis wind turbine with three blades. The blade
dynamics are represented by the following functions (Anderson et al., 1983),
VW
γ =
wB
1
Cp = (γ − 0.022 β p 2 − 5.6)e −0.17γ
2
1
PW = ρAC p VW 3 (6.2)
2
where wB is the blade angular velocity, γ is the tip speed ratio, βp is the blade pitch
angle, Cp is the dimensionless power coefficient, ρ is air density, and A is blade
impact area. PW is the resultant mechanical power which is extracted from the wind.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
v s = R s i s + d ϕ s / dt + jwa ϕ s
0 = R r1 i r1 + d ϕ r1 / dt + j ( w a − w)ϕ r1 + Rc (i r1 + i r 2 )
0 = R r 2 i r 2 + d ϕ r 2 / dt + j ( wa − w)ϕ r 2 + Rc (i r1 + i r 2 )
ϕ s = L s i s + Lm (ir1 + ir 2)
ϕ r1 = Lr1 i r1 + Lm i s + L12 i r 2
ϕ r 2 = Lr 2 i r 2 + Lm i s + L12 ir1
TE = (3 / 2) Pϕ s × is
TE − TL = ( J / P)dw / dt (6.3)
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Stator equations:
Vq = − Ra iq + e ′q′ − X d′′ i d
Vd = − Ra i d + e d′′ − X q′′i q
de q′′
Td′′0 = e ′q − e q′′ − ( X d′ − X d′′ )i d
dt
de ′q X d − X d′
Td′ 0 = V f − e q′ − (e ′q − e ′q′ )
dt X d′ − X d′′
de d′′
Tq′′0 = e ′d − e ′d′ − ( X q′ − X q′′ )iq
dt
de d′ X q − X q′
Tq′0 = −e d′ − (e d′ − e d′′ )
dt X q′ − X q′′
T ′ = e ′d′ i d + e ′q′ i q + ( X q′′ + X d′′ )i d i q (6.4)
Rotor equation:
d 2δ dδ
M +D = TM − TE (6.5)
dt 2 dt
Time domain simulation studies are carried out on wind farm integrated
power system installed with GUPFC, which is shown in Figure 6.1. The system is
kept as simple as possible and grid data are inspired from IEEE first benchmark
model (IEEE, 1997). Series converters VSC2 and VSC3 are inserted into Lines 2 and
1, respectively. Shunt converter (VSC1) is connected to Bus 1.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
e(k ) = ∆P + K w ∆w (6.7)
where Kw is the damping gain. Since aggregated synchronous machine model is used,
w and wref represents the speed at sample-k, and base speed of all parallel operating
generators, respectively. As opposed to one of the originally proposed fuzzy inputs in
the paper (Mudi et al., 1999), control system is made insensitive to noise in the error
measurement using error-integral instead of error-derivative which lessen control
signal oscillations highly observed in simulation cases. In this case, the error-integral
at sample-k can be computed as
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
It is important to note that the series converter of the GUPFC, where STFDC is not
utilized, controls real power flow on Line-1 using equation (6.6) with auxiliary
damping signal, as shown in Figure 6.1. STFDC is the alternative of this control
mode and constructed from a fuzzy damping controller (FDC) and a fuzzified gain
tuner (FGT), as shown in Figure 6.1.
In FDC scheme, the signals e and Σe in equations (6.7) and (6.8) are
respectively multiplied by gains (a1, a2), which needs to be optimized. Crisp values
are then mapped to their equivalent fuzzy values by the membership functions of
knowledge base in Figure 6.3. Membership functions for eO and ΣeO are symmetrical
triangles (except the two at both ends) which have equal 50% base overlap, divides
the domain [-1,1] into 7 equal regions. The term sets of eO and ΣeO contain the same
linguistic expressions for the magnitude part of the linguistic values and
characterizes rule matrix-1 in Figure 6.3, which contains 49 rules. The cell defined
by the intersection of the first row and the first column represents a rule such as, {“If
ΣeO is P1 and eO is N2 then ΔVq is N1”}. The antecedents are evaluated by applying
“min” operator and the output fuzzy set is truncated by applying “min” implication
operator. The fuzzy sets are aggregated into a single fuzzy set by “max” operator that
should be later dezuffied to resolve a single real number for each output variable.
Centroid defuzzification method is applied to get incremental change in series
converter voltage as in equation (6.9):
∑i49=1 bi ∫ µ (i)
∆Vq (k ) = 49
(6.9)
∑ ∫ µ (i )
i =1
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
where µ(i) and bi are the output membership function and the center of output
membership function of the consequent of rule i, respectively. Finally, at sample-k,
q-axis component of the series converter voltage for oscillation damping (as well as
for dynamic real power flow control) is calculated in equation (6.10) where β is the
gain factor at sample-k which is decided by FGT.
Vq (k ) = Vq (k − 1) + a 3 β ∆Vq (k ) (6.10)
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
The scaling factors (a1, a2,) are used to normalize input variables of the FDC.
{eO=a1e; ΣeO=a2Σe}. Similarly, FDC output variable (ΔVq) is first multiplied by a3
then tuned by FGT adaptively. Commonly, there is no well-defined method for
selection of scaling factors (Mudi et al., 1999). In this research, these parameters are
optimized by simplex method. The cost function is based on integral time absolute
error (ITAE) and given in equation (6.12) where t is the simulation time, t0 is the
fault time. T is the total simulation time for case 1 in the next section. PSCAD
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
configuration for this task is shown in Figure 6.5. The convergence performance of
cost function in simplex method is shown in Figure 6.6. The value of f is minimized
from 0.0720 to 0.0114 in 51 iterations for a tolerance of 1.0E-6 when only FDC is
executed while FGT is deactivated. The optimized parameters are listed in Table 6.1.
( )
T
f (a1 , a 2 , a 3 ) = ∫ t ⋅ wref − w ⋅ dt (6.12)
t =t0
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
The stability concern is first evaluated for three-phase and single-phase faults
without GUPFC in the power network and then with GUPFC. The dynamic
simulations investigate the impact of faults (i) on the stability of
synchronous/induction generators, (ii) on GUPFC performance when controlling real
and reactive power flows as well as AC bus voltage. PSCAD and MATLAB are used
simultaneously for simulating transient behavior of the models. The parameters of PI
controllers, shown in Figure 6.1, are given in Appendix C. The capacitance of DC
link is C=0.2 F. The performance of STFDC is examined for different disturbance
conditions which lead to local mode of oscillations in conjunction with the following
dynamic control tasks of the GUPFC:
• Line-2 real power flow (PL2) using either FDC or STFDC by VSC2
• Line-2 reactive power flow (QL2) by VSC2
• Line-1 real power flow (PL1) by VSC3
• Line-1 reactive power flow (QL1) by VSC3
• Bus 1 voltage (V1) by VSC1
• DC link voltage (E) by VSC1
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
control schemes. Although, STFDC is only activated for VSC2 and Line-2 reactive
power flow and Line-1 real and reactive power flows are controlled by simple PI
controllers, it is found that STFDC indirectly smoothens the variations of simulated
waveforms against fault and shows better performance than FDC in general. As
evidence by response curves depicted in Figure 6.7a, STFDC performance is superior
to FDC on SEDCIG rotor speed damping, being also better than that of PI controller.
In Figure 6.7b, STFDC responses better than FDC and PI controller in damping SG
oscillations with reduced undershoot/overshoot and less settling time. As the
consequence of the fault, real and reactive power flow variations of Line-1, presented
in Figures 6.7c and 6.7d, and those of Line-2 presented in Figures 6.7e and 6.7f are
minimized better by STFDC with less undershoot/overshoot compared with the FDC.
DC link voltage excursions of GUPFC for different damping control schemes are
depicted in Figure 6.7g and it is found that among the two control schemes, the ITAE
index is smaller for STFDC. In Figure 6.7h, PI controller settles Bus 1 voltage to its
controlled value of 1.0 pu with a smaller ITAE value in case of STFDC. Effect of
employing STFDC with optimized gains improves transient responses of both
SEDCIG speed and IG speed. This situation is illustrated on Figures 6.7i and 6.7j,
respectively. Voltage and current signals of the quasi multi-pulse converters after the
fault are presented in Figure 6.8. In more detail, simulated phase shift angles of
converters M and N and one selected GTO voltage are shown in Figure 6.9.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(c) Variation of Line-1 real power flow under different control modes
(d) Variation of Line-1 reactive power flow under different control modes
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(e) Variation of Line-2 real power flow under different control modes
(f) Variation of Line-2 reactive power flow under different control modes
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Figure 6.9. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(c) Variation of Line-1 real power flow under different control modes
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(d) Variation of Line-1 reactive power flow under different control modes
(e) Variation of Line-2 real power flow under different control modes
(f) Variation of Line-2 reactive power flow under different control modes
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(a) Real power output of the wind farm following three-phase fault
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(b) Reactive power output of the wind farm following three-phase fault
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
The system is subjected to phase-A to ground fault on Line-3 near Bus 1 for a
duration of 265 ms at 8.5 s. Pre-disturbance operating conditions are changed as;
PL1ref=1.0 pu PL2ref=0.75 pu, QL1ref=QL2ref=0.0 pu, Eref=2.0 kV, V1ref=1.0 pu. Figures
6.12a and 6.12b shows the transient fluctuations of the SEDCIG speed and SG speed,
respectively and provide a comparison between different control schemes. Besides,
rise time and settling time of FDC and STFDC is practically the same for both
generators, STFDC gives lower undershoot in case of SEDCIG and quantitative
comparison shows better STFDC results for oscillation damping of SG speed. The
waveforms in Figures 6.12c-f indicate that STFDC is again found to be superior to
FDC in general when controlling real and reactive power flows of the lines after the
fault both with reduced overshoot/undershoot characteristics and with smaller ITAE
indices. Although undershoot in case of STFDC exceeds the undershoot in case of
FDC by approximately 4.5% in Figure 6.12e, the steady-state error is more
effectively minimized by STFDC and a minimum ITAE index is reached. DC
voltage regulation of the GUPFC is satisfactory in Figure 6.12g and STFDC reduces
DC voltage fluctuations significantly better than FDC. Figure 6.12h shows Bus 1
voltage variations following single-phase to ground fault. The AC voltage controller
is again satisfactory like in previous case studies and gives practically the same
response in case of FDC and STFDC with a better ITAE index than that of FDC.
(a) Transient response of SEDCIG speed without GUPFC and with GUPFC
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(c) Variation of Line-1 real power flow under different control modes
(d) Variation of Line-1 reactive power flow under different control modes
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(e) Variation of Line-2 real power flow under different control modes
(f) Variation of Line-2 reactive power flow under different control modes
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Case 2
Case 3
6.3.5. Discussion
The newly proposed damping controller is robust to change in fault type and
fault duration as well as robust to changing operating conditions of the power
system. Better damping characteristics for local mode of oscillations of SG are
achieved by GUPFC equipped with STFDC. Furthermore, STFDC can control
SEDCIG speed better than FDC in case of a fault although SEDCIG speed signal is
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
not measured in the proposed damping control scheme. The successful operation of
the shunt and series converters of the GUPFC is proven by maintaining constant DC
link voltage and after faults GUPFC shows stable operation and able to restore real
and reactive power flows of the transmission lines to their regulated values with
significantly less variations in case of STFDC. This situation can claim longer
transient fault duration that the system can withstand. It is also noted that shunt
reactive power support of GUPFC improves voltage profile of the wind farm bus
during transient conditions.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Figure 6.13. Two-Area System embedded with IPFC and its control scheme
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
The scaling factors (a1, a2, and a3) in STFDC configuration for GUPFC
should be re-optimized using simplex method to normalize input and output variables
of the STFDC, since a different type of multi-converter FACTS device is embedded
into a different power system. The cost function is based on ITAEs of different
measured generator speeds given in equation (6.13) where w1, w2, and w3 are the
speeds of G1, G2, and G3 in Figure 6.13, respectively. For IPFC, the value of f is
minimized from 0.2078 to 0.0399 in 97 iterations for a tolerance of 1.0E-6 as shown
in Figure 6.15a. Similarly, for SSSC, the value of f is minimized from 0.2452 to
0.2221 in 60 iterations for a tolerance of 1.0E-6 as shown in Figure 6.15b. Simplex
method is run when only FDC is executed while FGT is deactivated for both FACTS
devices. The optimized parameters are listed in Table 6.3.
f (a1 , a2 , a3 ) = ∫ (t ⋅ w1 − w2 + t ⋅ w1 − w3 )⋅ dt
T
(6.13)
t =t0
The stability of the Two-Area System is investigated without and with IPFC
having STFDC by applying different types of faults with different durations.
Moreover the damping feature of IPFC is compared with that of SSSC for all cases
under the same control scheme. The impact of faults is also investigated on the
performances of control loops of IPFC which is shown in Figure 6.13. PSCAD
having a solution time step of 100 μs and MATLAB are communicated on-line for
simulating transient behavior of the models. The chosen parameters of the PI
controllers for the IPFC are given in Appendix C. The capacitance of DC link is
C=0.2 F. Steady-state uncontrolled real power flows of the intertie are 0.975 pu for
each transmission line. IPFC is activated for both Lines 1-2 when switch sw1 and
sw3 are opened and sw2 is closed. SSSC is activated on Line-2 when switch sw2 and
sw3 are opened and sw1 is closed. The performance of STFDC for both IPFC and
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
SSSC is examined individually for the same disturbance conditions applied to Two-
Area System which lead to inter-area mode of oscillations in conjunction with the
following dynamic control tasks of the IPFC and SSSC:
SSSC
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Before applying disturbance, the reference values of tie-line flows, PLine-1 and
PLine-2 are respectively set to 1.1 pu and 1.2 pu at the real power flow controllers of
IPFC while the DC link voltage is regulated at 1.4 kV. The same reference value of
PLine-2 is set for SSSC’s real power flow controller. Then a three-phase to ground
fault near Bus 1 on Line-1 with 140 ms duration is applied at t=2.0 s. As shown in
Figures 6.16a and 6.16b, the angle oscillations of generators G2 and G3 with respect
to generator G1 are cumulative and lead to unstable operation when no FACTS
device is activated. SSSC having only VSC2 exhibits weakly damped inter-area
modes at approximately 0.50 Hz for both G2 and G3 with respect to G1. On the other
hand, IPFC, having both VSC1 and VSC2, effectively damps out the oscillations
caused by this severe disturbance in relatively short duration. Comparing the
responses of IPFC to the SSSC compensation scheme in Figures 6.16c and 6.16d, the
positive contribution of the proposed STFDC adapted for IPFC is clear when
controlling intertie real power flows caused by inter-area oscillations. Figure 6.16e
shows that the time responses of the DC link voltage of both SSSC and IPFC are
practically the same which is highly required for proper VSC operation. Figure 6.16f
shows reactive power flow fluctuations on Line-1 caused by three-phase disturbance
when reactive power flow control function of IPFC is disabled to make a fair
comparison to SSSC. Figures 6.16g and 6.16h show that STFDC equipped IPFC
better improves bus voltage profiles of the intertie with smoother responses
following three-phase fault when compared with STFDC equipped SSSC. Figures
6.17 and 6.18 shows some selected time domain signals of the two VSCs of IPFC
which reveal stable converter operation.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
when there is no compensation is applied. Figures 6.19a and 6.19b show the
responses of the generators G2 and G3 with respect to generator G1 when SSSC with
STFDC are applied and when IPFC with STFDC are applied. The comparative time-
domain results show that the stabilizing function of IPFC for inter-area oscillations is
superior to those of SSSC even STFDC is adapted individually to both FACTS
devices by optimizing its scaling factors. IPFC with STFDC easily stops the real
power oscillations both on Lines 1 and 2 and forces them to their steady-state
controlled values as shown in Figures 6.19c and 6.19d. When a particular
comparison between Figures 6.16c and 6.19c is made, SSSC weakly suppresses
power oscillation in case of two-phase to ground fault due to longer duration of fault.
DC link voltage controllers of both SSSC and that of IPFC gives practically the same
response to the short circuit as shown in Figure 6.19e. Figure 6.19f shows reactive
power flow fluctuations on Line-1 when IPFC and SSSC are operated separately
when reactive power flow control function of IPFC is disabled. Accordingly, as in
case 1 the fluctuations are less as in case of IPFC when compared with SSSC.
Figures 6.19g and 6.19h show that STFDC equipped IPFC better improves bus
voltage profiles of the intertie with smoother responses following two-phase fault
when compared with STFDC equipped SSSC.
(a) Generator G2 rotor angle measured with respect to generator G1 rotor angle
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(b) Generator G3 rotor angle measured with respect to generator G1 rotor angle
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(e) DC link voltage excursions of two FACTS devices following three-phase fault
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Figure 6.18. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(a) Generator G2 rotor angle measured with respect to generator G1 rotor angle
(b) Generator G3 rotor angle measured with respect to generator G1 rotor angle
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(e) DC link voltage excursions of two FACTS devices following two-phase fault
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
shows that IPFC with STFDC robustly stabilizes the inter-area mode of oscillations
while SSSC with STFDC shows a poor suppressing function. Figures 6.20c and
6.20d show that IPFC endowed with the proposed STFDC eliminates the oscillations
of the real power transmission of Line-2, between the two areas, and resumes the real
power transmission to its controlled level before the fault. Figure 6.20e indicates that
the DC link voltage controllers of both SSSC and that of IPFC gives practically the
same response to the short circuit as in previous fault cases. Figure 6.20f shows
reactive power flow fluctuations on Line-1 when IPFC and SSSC are operated
separately when reactive power flow control function of IPFC is disabled as in
previous fault scenarios. It is shown that the reactive power fluctuations are
practically the same for two FACTS devices. Figures 6.20g and 6.20h show that
STFDC equipped IPFC better improves bus voltage profiles of the intertie with
smoother responses following single-phase fault when compared with STFDC
equipped SSSC.
(a) Generator G2 rotor angle measured with respect to generator G1 rotor angle
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(b) Generator G3 rotor angle measured with respect to generator G1 rotor angle
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
(e) DC link voltage excursions of two FACTS devices following single-phase fault
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Table 6.4 summarizes voltage distortions of the intertie buses, namely Buses
1 and 2, as a measure of THD. Records of the simulated cases taken at 12.5 s show
that THD values are within acceptable limits when STFDC is activated in both
control loops of IPFC and SSSC (IEEE, 1993). Consequently, filtering is not
required for the two FACTS devices even GTOs are switched at fundamental system
frequency.
SSSC
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6.4.4. Discussion
The originally proposed STFDC for one of the series converters of the
GUPFC is adapted for one of the IPFC’s converters and SSSC by changing one of
the inputs of the fuzzy interface and re-optimizing the scaling factors of the STFDC.
STFDC is robust to change in fault-type and fault duration while damping inter-area
mode of oscillations in Two-Area System. IPFC equipped with STFDC mitigates
better angle oscillations of the generators than SSSC equipped with STFDC.
Moreover, IPFC can control line real power flows of the intertie better than SSSC in
case of faults. These results show that IPFC shows superior control characteristics,
owing to the fact that IPFC has more control degrees of freedom than SSSC.
Although there is no voltage control function is included either to IPFC or SSSC
operations, both are able to make voltages of the intertie buses less oscillatory in case
of severe faults. Successful operations of the IPFC and SSSC are proven by
maintaining constant DC link voltage under fault scenarios.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Power system and BtB-STATCOM having two quasi multi-pulse VSCs, and
control blocks are simulated in PSCAD with a solution time step of 100 µs. Each
VSC of BtB-STATCOM is rated at 100 MVA. Each single-phase three-winding
transformer in twelve-pulse converter unit is rated at 60 Hz, 8.33 MVA, 20/2/1.1548
kV with a leakage reactance of j0.1 pu. Each single-phase transformer of summing
and magnetic interface is rated at 60 Hz, 16.67 MVA, 137.92/38 kV, j0.1 pu.
The stability of the SMIB system is investigated without and with BtB-
STATCOM having the PI control schemes shown in Figure 6.21 by applying
different types of faults with different durations. The damping ability of BtB-
STATCOM is evaluated for all cases with this respect. The impact of faults is also
investigated on the performances of control loops of BtB-STATCOM. PSCAD
having a solution time step of 100 μs is used for simulating transient behavior of the
SMIB system embedded with BtB STATCOM. The chosen parameters of the PI
controllers for BtB-STATCOM are given in Appendix C. The capacitance of DC link
is C=0.2 F. Using switches sw1 and sw2, BtB-STATCOM can be bypassed with a
line, required for the simulation cases. For instance, when sw1 is closed while sw2 is
opened, BtB-STATCOM is bypassed by a short line. When sw1 is opened while sw2
is closed, BtB-STATCOM is in operation alternatively. The following dynamic
control tasks of the BtB-STATCOM are examined for different disturbance
conditions:
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
195
6. TRANSIENT STABILITY STUDIES A. Mete VURAL
196
6. TRANSIENT STABILITY STUDIES A. Mete VURAL
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Figure 6.24. Simulated phase shift angles (ɸM and ɸN) and one GTO voltage
In this case, a relatively longer three-phase to ground fault is applied near Bus
2 (infinite bus) in Figure 6.21. The fault is lasted for 160 ms. Simulated waveforms
of the power system configuration embedded with BtB-STATCOM following the
disturbance are presented in Figure 6.25. The speed oscillations of the SG like the
one in previous case study are observed in Figure 6.25a when BtB-STATCOM is
deactivated. The oscillation duration is relatively shorter than that of previous case
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
since there is short line between SG and the fault location. When BtB-STATCOM is
activated, SG speed oscillation is better damped out when compared with the
previous case study. Moreover the slight drop in speed is not observed following
three-phase fault. This is due to the fact that the fault is occurred near a stiff bus and
BtB-STATCOM isolates the disturbance from SG with its converters. The same
steady-state speed difference of the SG (0.0015 pu) is observed like the one in
previous case study, due to the same loading condition of the SG as expected. In
Figure 6.25b, the maximum overshoot of the controlled SG real power output (0.8
pu) is significantly reduced in this case with a better response of the BtB-STATCOM
to the fault. The DC link voltage fall in Figure 6.25c is unavoidable. However, as
soon as the fault is cleared, DC link voltage restores to its reference without affecting
BtB-STATCOM operation. Reactive power demand of the SG in Figure 6.25d
restores immediately to its pre-fault value as soon as the fault is cleared. A less
undershoot shows up than that of previous case due to the fault isolation feature of
the BtB-STATCOM. Figures 6.25e and 6.25f depicts that the dynamic voltage
support within the study system is effectively provided by BtB-STATCOM at two
neighboring buses under the three-phase fault. In detail, the drop in Bus 2 voltage is
not avoided. However the voltage is controlled with less overshoot when BtB-
STATCOM is activated.
199
6. TRANSIENT STABILITY STUDIES A. Mete VURAL
200
6. TRANSIENT STABILITY STUDIES A. Mete VURAL
201
6. TRANSIENT STABILITY STUDIES A. Mete VURAL
Case 1
Case 2
V1(L-L) V2(L-L) V1(L-L) V2(L-L)
1.38 % 1.36 % 1.37 % 1.36 %
6.5.3. Discussion
6.6. Summary
In this chapter, strong control capability of the GUPFC with regulating multi-
line flows and bus voltage is extended with an optimized self-tuned fuzzy control
scheme for oscillation damping in a wind farm integrated power system. It is shown
both graphically and quantitatively that the proposed damping scheme is robust in its
performance over a range of disturbance conditions and does not only improves
transient stability of induction/synchronous generators but also assists indirectly to
other GUPFC control functions which are tightly interacted with each other. The
proposed control scheme is model independent since the design is based on
instantaneous system states rather than system parameters. With the inclusion of
quasi-multi pulse converters switching at 60 Hz into the grid, harmonic content
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
complies with the regulations. Hence, no filter is required for harmonic reduction at
the line side of the GUPFC converters.
Multi-line power flow control function of IPFC is extended with the
optimized self-tuned fuzzy control scheme, originally proposed for GUPFC, to
robustly mitigate inter-area mode of oscillations of a multi-machine power system
having two remote areas which are tied by double transmission circuit. The
performance of the damping scheme is verified graphically using time domain
instantaneous responses of the system states to various faults. As also shown in
GUPFC based transient stability studies, the proposed damping scheme assists
indirectly to the other real power flow control loop of the IPFC where damping
scheme is not utilized. The robustness of the proposed fuzzy damping scheme is
further verified by adapting it to the real power flow control loop of SSSC, which
yield particular performance comparison between IPFC and SSSC. The quasi-multi
pulse converters of the FACTS devices do not disturb power quality in terms of
harmonic content, which complies with the regulations. Hence, no filter is required at
the line side of the converters.
Multi-control function of BtB-STATCOM is examined without any damping
control scheme for improving power system stability considering various faults with
different locations and durations. The obtained results confirm that the real power
transfer controller of PI type of BtB-STATCOM can provide adequate damping of
generator speed oscillations owing to the segmentation of the power system with the
DC link of BtB-STATCOM. At the same time, it is ensured that all BtB-STATCOM
control loops are working truly without losing stability under different fault
scenarios. Voltage profiles of the neighboring buses are also improved with fast and
independent reactive power support of BtB-STATCOM converters in both steady-
and transient states.
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6. TRANSIENT STABILITY STUDIES A. Mete VURAL
204
7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL
205
7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL
In the work reported in this thesis, a review of the state of the art is introduced
based on the simplified power circuit configuration and operating characteristics of
the first and the second generation of FACTS devices ranging from single- to multi-
converter topologies.
Power flow (load flow) analysis is an important tool for power system
planning in which the transmission constraints can also be determined in a given
network. Power flow solution gives information about the magnitude and phase
angle of the voltage at each bus as well as real and reactive power flows in each line
for given generation, load, and transmission network data of a power system. In this
context, the steady-state models of the GUPFC, IPFC, and BtB-STATCOM are
proposed and designed in PSCAD environment even PSCAD is primarily aimed to
simulate transient responses of the power system components. Developed models are
verified in various multi-bus power systems to demonstrate the capability of steady-
state controls of the real and reactive power flows on transmission lines as well as to
regulate system bus voltage. Steady-state models of STATCOM, SSSC, and UPFC
are also developed. Particular performance comparison is made between the
aforementioned FACTS devices. The advantage of this approach is fast, modular and
requiring no programming effort to include power injections and their derivatives
with respect to the state variables power system, such as bus voltages and their
respective phase angles, at the suitable locations of the Jacobian matrix and
mismatch vector. It is concluded that as long as the operational and control
constraints are satisfied, theoretically there is no limit in the number of VSCs which
are employed for building up the FACTS device. The method can suffer from long
computation time and may require high CPU computing power with large memory if
many multi-converter FACTS devices are embedded into relatively large power
systems having many buses.
In this thesis, eight two-level force-commutated converters are joined
together using magnetic interfaces to realize quasi multi-pulse converter operation
for multi-converter FACTS device applications. The quasi multi-pulse converter is
the building block of converter-level modeling studies of the multi-converter FACTS
devices. Appropriate adjustment of individual phase-shifted angles of the two groups
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7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL
of series converters makes it possible to independently control the amplitude and the
phase of the AC voltage of the quasi multi-pulse converter. The quasi multi-pulse
converter based GUPFC, IPFC, and BtB-STACOM are successfully modeled in
PSCAD, including a detailed representation of the simulation design parameters. The
presented time-domain simulation results verify adequate operations of the GUPFC,
IPFC, and BtB-STATCOM separately, as well as demonstrating the successful
operations of the designed controllers. The proposed converter-level models of the
multi-converter FACTS devices can be directly implemented in any software
package that has a graphical interface. The models are independent of the type of the
control schemes applied for any multi-converter FACTS device.
The simplex optimization method and fuzzy logic techniques are used in
designing controllers of the multi-converter FACTS devices for various control
purposes. In the simplex optimization method, the cost function is minimized to
optimize single- and multi-controllers of the concerned multi-converter FACTS
device. Fuzzy logic theory is used to design two novel controllers for IPFC and
GUPFC, which are examined through time domain simulations of various case
studies applied in a variety of power systems. The first novel controller is based on
the combination of a conventional PI controller and a Mamdani-type fuzzy inference
system for the quasi multi-pulse IPFC, designed for high performance decoupling
action between controlled real and reactive power flows of a transmission line. In
general this control scheme can be employed in any series converter of the multi-
converter FACTS device, for instance UPFC or GUPFC to relieve inherent real and
reactive power flow coaction. On the contrary of analytically decoupled gain design,
the proposed control scheme is robust and does not rely on system mathematical
model. Consequently it adapts itself to parameter variations in the power system and
performs better. There is also an option to activate fuzzy component only when a
change in either real or reactive power flow command occurs. Such coordination can
yield improved rise time and settling time for start-up transients in simulation
environment.
Low frequency generator oscillations are commonly experienced due to
severe disturbances in the form of either local mode or inter-area mode of
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7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL
208
7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL
The controllers designed in this work are general and can be applied to other
FACTS devices easily. The results and discussions presented in this thesis will
provide valuable information to electric power utilities/companies in the near future
that are engaged in the planning and operation of the FACTS devices in Turkey
where mostly few STATCOM installations are reported.
This thesis reveals the potential usage and benefits of GUPFC, IPFC, and
BtB-STATCOM applications for intelligent control of future grids having distributed
energy resources, with emphasis on high power applications of converters with low
THD. Further research can be carried out in the following paragraphs:
209
7. CONCLUSIONS AND FUTURE WORK A. Mete VURAL
210
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226
CIRRICULUM VITAE
Education:
PhD Electrical and Electronics Çukurova University 2009-…..
Engineering
Msc Electrical and Electronics University of Gaziantep and 1999-2001
Engineering University of Strathclyde
(as visitor scholar in 2000)
Bsc Electrical and Electronics University of Gaziantep 1995-1999
Engineering
Work Experience:
Hasan Kalyoncu University, Electrical and Full-time July-2011 / present
Electronics Engineering Department instructor
Atılım University, Electrical and Full-time Sept-2008 / June-2011
Electronics Engineering Department instructor
Wuppertal University, Automation and Research Nov-2004 / Mar-2007
Control Engineering Department,Germany assistant
Gaziantep University, Electrical and Research Aug-1999 / Nov-2004
Electronics Engineering Department assistant
Research Interests:
• Modeling and control of FACTS devices
• Computational intelligence applications to FACTS device control
• Power system simulation
Professional Activities:
• Refereeing
International Journal of Electrical Power and Energy Systems
IET Generation, Transmission & Distribution
Turkish Journal of Electrical Engineering & Computer Sciences
Journal of Electrical and Electronics Engineering Research
World Journal of Modeling and Simulation
Journals of Zhejiang University-Science-C (Computers & Electronics)
Ain Shams Engineering Journal
• IEEE student member since 1999
• EMO member since 1999
227
Given Courses:
EE 451 - Power System Analysis
EE 452 - High Voltage Techniques
EE 450 - Electrical Machinery and Drives
EEE 101 - Introduction to Electrical and Electronics Engineering
EEE 120 - Introduction to MATLAB
EEE 201/202 - Circuit Analysis I-II
EE 203 - Digital Circuits and Systems
EE 403 - Communication Networks
EE 491/492 - Design Project I-II
MATH 151 - Calculus I
Publications:
• Journals (SCI-E)
VURAL A.M., BAYINDIR K.Ç., 2012. Transient stability enhancement of the power
system interconnected with wind farm using generalized unified power flow
controller with simplex optimized self-tuning fuzzy damping scheme,
International Review of Electrical Engineering, vol. 7, no. 4, pp. 5091-5107.
VURAL A.M., BAYINDIR K.Ç., 2012. A hybrid fuzzy-PI control scheme for a quasi
multi-pulse interline power flow controller including PQ decoupling feature,
Journal of Power Electronics, vol. 12, no. 5, pp. 787-799.
VURAL A.M., BAYINDIR K.Ç., 2011. Two-level quasi multi-pulse voltage source
converter based generalized unified power flow controller, International
Review of Electrical Engineering, vol. 6, no. 5, pp. 2622-2637.
VURAL A.M., TÜMAY M., 2007. Mathematical modeling and analysis of a unified
power flow controller: A comparison of two approaches in power flow studies
and effects of UPFC location, International Journal of Electrical Power &
Energy Systems, vol. 29, issue 8, pp. 617-629.
TÜMAY M., VURAL A.M., LO K.L., 2004. The effect of unified power flow
controller (UPFC) location in power systems, International Journal of
Electrical Power & Energy Systems, vol. 26, issue 8, pp. 561-569.
VURAL A.M., TÜMAY M., 2004. Analysis and modeling of unified power flow
controller: Modification of Newton-Raphson algorithm and user-defined
228
modeling approach for power flow studies, Arabian Journal for Science and
Engineering, vol. 29, no: 2B, pp. 135-153.
TÜMAY M., VURAL A.M., LO K.L., 2005. Simulation of unified power flow
controller by using modified power injection model, Iranian Journal of
Science and Technology, vol. 29, pp. 49-64.
• Journals
• International Conferences
VURAL A.M., BAYINDIR K.Ç., 2012. Converter level modeling and control of
quasi multi-pulse static synchronous series compensator, IEEE Symposium
on Electrical and Electronics Engineering, EEESYM’2012, pp. 698-702.
VURAL A.M., BAYINDIR K.Ç., 2012. Understanding the steady-state modeling and
analysis of power systems embedded with VSC-based FACTS devices, IEEE
EnergyTech2012.
229
VURAL A.M., BAYINDIR K.Ç., 2010. Optimization of parameter set for
STATCOM control system, IEEE PES, Transmission and Distribution
Conference and Exposition, pp. 1-6.
VURAL A.M., TÜMAY M., 2003. Steady state analysis of unified power flow
controller: Mathematical modeling and simulation studies, IEEE Powertech
Conference, vol. 4.
EKER İ., VURAL A.M., 2003. Experimental on-line identification of a three-mass
mechanical system, IEEE Conference on Control Applications, vol. 1, pp. 60-
65.
VURAL A.M., TÜMAY M., 2003. Power flow analysis of power system embedded
with UPFC using Psasp program, International Conference on Electrical and
Electronics Engineering, ELECO’2003, pp.22-26.
EKER İ., VURAL A.M., SÜSLÜOĞLU B., 2003. Experimental identification of an
electromechanical system running in open-loop conditions, International
Conference on Electrical and Electronics Engineering, ELECO’2003, pp.
284-288.
VURAL A.M., TÜMAY M., 2001. UPFC for controlling power flow in power
systems, International Conference on Electrical and Electronics Engineering,
ELECO’2001, pp. 1-4.
VURAL A.M., EKER İ., 2004. Parameter identification of a permanent magnet DC
motor: An experimental approach, International Conference on Electrical
Machines, ICEM’2004, paper no. 104.
• National Conferences
230
VURAL A.M., EKER İ., SÜSLÜOĞLU B., 2003. Doğal mıknatıslı bir DC
motorun deneysel olarak tanılaması, 10. Ulusal Elektrik-Elektronik-Bilgisayar
Mühendisliği Kongresi, İstanbul, pp. 122-125.
VURAL A.M., EKER İ., 2003. Least squares on-line identification of a dc
motor, Mühendislik Bilimleri Genç Araştırmacılar 1. Kongresi, İstanbul, pp. 183-
190.
VURAL A.M., TÜMAY M., MA T.T., 2001. Güç sistemlerindeki güç
akışının UPFC ile kontrolü, 9. Ulusal Elektrik-Elektronik-Bilgisayar Mühendisliği
Kongresi, Bursa, pp. 196-199.
231
232
APPENDIX
233
APPENDIX A: Converter Design Data for Power Flow Studies
234
APPENDIX B: Test Systems Data
B1. WSCC 3-Machine 9-Bus System (230 kV, 60 Hz, 100 MVA base)
Generation Data:
Generator No: Location Voltage: Real MW
1 Bus 1 16.5 kV Swing Bus
2 Bus 2 18.0 kV 163
3 Bus 3 13.8 kV 85
Transformer Data:
Transformer No: Location Tap: X (pu)
1 Bus 1-Bus 4 16.5 / 230 kV 0.0576
2 Bus 2-Bus 7 18.0 / 230 kV 0.0625
3 Bus 3-Bus 9 13.8 / 230 kV 0.0586
Load Data:
Load No: Location Real MW Reactive MVAR
1 Bus 5 125 50
2 Bus 6 90 30
3 Bus 8 100 35
Line Data:
Line No: Location: R (pu) X (pu) B/2 (pu)
1 Bus 4-Bus 5 0.01000 0.08500 0.04400
2 Bus 4-Bus 6 0.01700 0.09200 0.03950
3 Bus 5-Bus 8 0.03200 0.16100 0.07650
4 Bus 6-Bus 9 0.03900 0.17000 0.08950
5 Bus 7-Bus 8 0.00850 0.07200 0.03725
6 Bus 8-Bus 9 0.01190 0.10080 0.05225
235
B2. IEEE 14-Bus System (230 kV, 60 Hz, 100 MVA base)
Generation and Load Data:
Bus Generation: Bus Load:
Bus No:
Real Reactive Real Reactive
MW MVAR MW MVAR
1 232.4 -16.9 0.0 0.0
2 40.0 42.4 21.7 12.7
3 0.0 23.4 94.2 19.0
4 0.0 0.0 47.8 -3.9
5 0.0 0.0 7.6 1.6
6 0.0 12.2 11.2 7.5
7 0.0 0.0 0.0 0.0
8 0.0 17.4 0.0 0.0
9 0.0 0.0 29.5 16.6
10 0.0 0.0 9.0 5.8
11 0.0 0.0 3.5 1.8
12 0.0 0.0 6.1 1.6
13 0.0 0.0 13.5 5.8
14 0.0 0.0 14.9 5.0
Line Data:
Line No: Location: R (pu) X (pu) B/2 (pu)
1 Bus 1-Bus 2 0.01938 0.05917 0.02640
2 Bus 2-Bus 3 0.04699 0.19797 0.02190
3 Bus 2-Bus 4 0.05811 0.17632 0.01870
4 Bus 1-Bus 5 0.05403 0.22304 0.02460
5 Bus 2-Bus 5 0.05695 0.17388 0.01700
6 Bus 3-Bus 4 0.06701 0.17103 0.01730
7 Bus 4-Bus 5 0.01335 0.04211 0.00640
8 Bus 7-Bus 8 0.00000 0.17615 0.00000
9 Bus 7-Bus 9 0.00000 0.11001 0.00000
10 Bus 9-Bus 10 0.03181 0.08450 0.00000
11 Bus 6-Bus 11 0.09498 0.19890 0.00000
12 Bus 6-Bus 12 0.12291 0.25581 0.00000
13 Bus 6-Bus 13 0.06615 0.13027 0.00000
14 Bus 9-Bus 14 0.12711 0.27038 0.00000
15 Bus 10-Bus 11 0.08205 0.19207 0.00000
16 Bus 12-Bus 13 0.22092 0.19988 0.00000
17 Bus 13-Bus 14 0.17093 0.34802 0.00000
Transformer Data:
Transformer No: Location: Tap: X (pu)
1 Bus 4-Bus 7 0.978 0.20912
2 Bus 4-Bus 9 0.969 0.55618
3 Bus 5-Bus 6 0.932 0.25202
• Condenser is connected at Bus 8 to regulate bus voltage at 1.09 pu
• Shunt capacitance of 2.6465 µF is connected at Bus 9
236
B3. 3-Machine 7-Bus System (154 kV, 50 Hz, 100 MVA base)
Generation and Load Data:
Bus Generation: Bus Load:
Bus No:
Real Reactive Real Reactive
MW MVAR MW MVAR
1 317.8 369.4 0.0 0.0
2 50.0 0.0 200 150
3 0.0 0.0 0.0 0.0
4 50.0 0.0 200 150
5 0.0 0.0 0.0 0.0
6 0.0 0.0 0.0 0.0
7 0.0 0.0 0.0 0.0
Line Data:
Line No: Location: R (pu) X (pu) B/2 (pu)
1 Bus 1-Bus 2 0.0075 0.1324 0.04340
2 Bus 1-Bus 5 0.00000 0.00099 0.00000
3 Bus 1-Bus 4 0.00476 0.08390 0.02750
4 Bus 2-Bus 3 0.00527 0.09276 0.03030
5 Bus 2-Bus 3 0.00527 0.09276 0.03030
6 Bus 3-Bus 4 0.00527 0.09276 0.03030
7 Bus 3-Bus 4 0.00527 0.09276 0.03030
8 Bus 2-Bus 6 0.00000 0.00020 0.00000
9 Bus 4-Bus 7 0.00000 0.00020 0.00000
B4. 4-Machine 4-Bus System (154 kV, 50 Hz, 100 MVA base)
G1 and G3 terminal voltage is 1.0 pu with a phase shift of 0.0º. G2 and G4 terminal
voltage is 0.974 pu with a phase shift of 10.0º. Series inductive reactances of all
generators are 0.0265 pu. Each transmission line is identical having
resistance=0.01938 pu, inductive reactance=0.05917 pu, susceptance =0.0528 pu.
B5. Wind Farm Integrated Power System (154 kV, 60 Hz, 100 MVA)
Wind turbine parameters: 2.5 MVA, rated angular mechanical speed= 20 Hz, ρ =
1.225 kg/m3, A= 5026 m2 with a rotor radius of 40 m, gear box efficiency = 97 %,
gear ratio (machine/turbine) = 55.
SEDCIG parameters: 2.5 MVA, 0.86 pf lagging (without fixed capacitors),
VLL=13.8 kV, base angular frequency=60 Hz, Rs = 0.066 pu, Rr1= 0.298 pu,
Rr2=0.018 pu, Ls = 0.046 pu, Lm = 3.86 pu, Lr1=0.122 pu, Lr2 = 0.105 pu, J=2H=3.40
237
s, mechanical damping = 0.01 pu. 20 SEDCIGs are operated in parallel to give 50
MVA output.
SG parameters: 120 MVA, VLL=13.8 kV, base angular frequency=60 Hz, pf=
0.9957, H = 3.117 s, mechanical windage and friction loss = 0.04 pu, iron loss = 300
pu, Ra = 0.0025 pu (armature time constant, Ta = 0.278 s), Xd = 1.014 pu, X'd = 0.314
pu, T'd0 = 6.55 s, X''d = 0.280 pu, T''d0 = 0.039 s, Xq = 0.770 pu, X''q = 0.375 pu T''q0
= 0.071 s, potier reactance Xp = 0.163 pu, air gap factor = 1.0, number of Q-axis
damper windings = 1.
IEEE type 2 hydro governor and turbine parameters: for controller: real pole
gain = 0.88, proportional gain = 3.7, integral gain = 0.44, real pole time constant =
0.02 s, Turbine lead time constant = 0.01 s, turbine lag time constant =0.01 s,
governor time constant =0.05 s, inverse gate velocity limit =4.8 s/pu, gate velocity
time constant =0.1 s, permanent droop gain =0.08, gate position control rate limit =
0.22 pu/s, temporary droop gain = 0.0, temporary droop time constant = 0.01 s,
conversion constant = 0.895, time constant for smoothing = 0.02 s.
IEEE type SCRX solid state exciter parameters: VLN = 7967 V, line current=5020
A, rectifier smoothing time constant = 0.02 s, controller lead/lag time constant =
1.5/1.0 s, exciter time constant = 0.02 s, exciter gain = 100 pu, min/max field voltage
= -+5 pu, reverse resistance = 15 KΩ.
238
APPENDIX C: PI Controller Parameters
• Power Flow Studies (Chapter 3)
239
Real power flow regulator : 0.06, 0.002
Reactive power flow regulator : 0.001, 0.008
IPFC (Figure 3.4d)
Series VSC-1
Reactive power flow regulator : 0.001, 0.004
Real power balance regulator : 0.00008, 0.004
Series VSC-2
Real power flow regulator : 0.001, 0.008
Reactive power regulator : 0.0001, 0.002
GUPFC (Figure 3.4f)
Shunt VSC
Voltage regulator : 0.001, 0.08
Real power balance regulator : 0.001, 0.004
Series VSC-1
Real power flow regulator : 0.001, 0.08
Reactive power regulator : 0.001, 0.04
Series VSC-2
Real power flow regulator : 0.001, 0.08
Reactive power regulator : 0.0001, 0.02
240
Shunt VSC-2
Real power transfer controller (Figure 5.33c): 0.8, 0.01
AC voltage controller (Figure 5.33d) : 0.8, 0.001
• Transient Stability Studies (Chapter 6)
Two-Area System
Proportional gain-Kp, integral time constant -τi
IPFC (Figure 6.13)
Lower Series VSC
DC link voltage controller : 0.1, 0.001
Real power controller : 0.2, 0.001
Damping gain (Kw) : 500
Upper Series VSC
Real power flow controller : 1.0, 0.001
SSSC Controllers (Figure 6.13)
Series VSC
DC link voltage controller : 0.1 0.001
Real power controller : 0.2, 0.001
Damping gain (Kw) : 500
SMIB System
Proportional gain-Kp, integral time constant -τi
BtB-STATCOM (Figure 6.21)
Series VSC1
AC voltage controller : 0.8, 0.01
241
Real power transfer controller : 0.8, 0.01
Series VSC2
AC voltage controller : 0.8, 0.01
DC voltage controller : 0.1, 0.1
APPENDIX D: Derivation of Maximum Power Injections for BtB-STATCOM
(Chapter 3)
The following derivations are made for ensuring maximum real power
transfer and maximum reactive power compensation at the same time for BtB-
STATCOM.
For VSC4;
Pinj 2 max = - 0.7071 pu (when real power transfer from VSC1 to VSC2)
Pinj 2 max = + 0.7071 pu (when real power transfer from VSC2 to VSC1)
242
APPENDIX E: Programming Scripts
% This m-file reads PSCAD "*.out" file and puts it in matrix form for Matlab
% written by A. Mete VURAL
% begin
% reading main "*.out" file
sepet = importdata('file_name_no.out'); % specify the output file name with number
extension obtained by saving the channels to disk in PSCAD
% reading input data
t=sepet.data(:,1); % 1st column: PSCAD simulation time
data_namesimcase=sepet.data(:,n); n is the column number of data in *.out file
% end
• Chapter 5
243
Name='fuzdec_3b'
Type='mamdani'
Version=2.0
NumInputs=4
NumOutputs=2
NumRules=98
AndMethod='min'
OrMethod='max'
ImpMethod='min'
AggMethod='max'
DefuzzMethod='centroid'
[Input1]
Name='perrdot'
Range=[-33 33]
NumMFs=7
MF1='n3':'trimf',[-44 -33 -22]
MF2='n2':'trimf',[-33 -22 -11]
MF3='n1':'trimf',[-22 -11 0]
MF4='z':'trimf',[-11 0 11]
MF5='p1':'trimf',[0 11 22]
MF6='p2':'trimf',[11 22 33]
MF7='p3':'trimf',[22 33 44]
[Input2]
Name='perr'
Range=[-21 21]
NumMFs=7
MF1='n3':'trimf',[-28 -21 -14]
MF2='n2':'trimf',[-21 -14 -7]
MF3='n1':'trimf',[-14 -7 0]
MF4='z':'trimf',[-7 0 7]
MF5='p1':'trimf',[0 7 14]
MF6='p2':'trimf',[7 14 21]
MF7='p3':'trimf',[14 21 28]
[Input3]
Name='qerrdot'
Range=[-40 40]
NumMFs=7
MF1='n3':'trimf',[-53.33 -40 -26.67]
MF2='n2':'trimf',[-40 -26.67 -13.33]
MF3='n1':'trimf',[-26.67 -13.33 1.776e-015]
MF4='z':'trimf',[-13.33 -4.441e-016 13.33]
MF5='p1':'trimf',[1.776e-015 13.33 26.67]
MF6='p2':'trimf',[13.33 26.67 40]
MF7='p3':'trimf',[26.67 40 53.33]
[Input4]
Name='qerr'
Range=[-35 35]
NumMFs=7
MF1='n3':'trimf',[-46.67 -35 -23.33]
MF2='n2':'trimf',[-35 -23.33 -11.67]
MF3='n1':'trimf',[-23.33 -11.67 -1.776e-015]
MF4='z':'trimf',[-11.67 1.11e-016 11.67]
244
MF5='p1':'trimf',[-1.776e-015 11.67 23.33]
MF6='p2':'trimf',[11.67 23.33 35]
MF7='p3':'trimf',[23.33 35 46.67]
[Output1]
Name='delvq'
Range=[-80 80]
NumMFs=7
MF1='n3':'trimf',[-106.7 -80 -53.32]
MF2='n2':'trimf',[-80 -53.32 -26.64]
MF3='n1':'trimf',[-53.32 -26.64 0]
MF4='z':'trimf',[-26.64 0 26.68]
MF5='p1':'trimf',[0 26.68 53.32]
MF6='p2':'trimf',[26.68 53.32 80]
MF7='p3':'trimf',[53.32 80 106.7]
[Output2]
Name='delvd'
Range=[-400 400]
NumMFs=7
MF1='n3':'trimf',[-533 -400 -266.8]
MF2='n2':'trimf',[-400 -266.8 -133.3]
MF3='n1':'trimf',[-266.8 -133.3 0]
MF4='z':'trimf',[-133.3 0 133.3]
MF5='p1':'trimf',[0 133.3 266.8]
MF6='p2':'trimf',[133.3 266.8 400]
MF7='p3':'trimf',[266.8 400 533]
[Rules]
7 7 0 0, 7 0 (1) : 1 0 0 7 7, 0 7 (1) : 1
7 6 0 0, 7 0 (1) : 1 0 0 7 6, 0 7 (1) : 1
7 5 0 0, 7 0 (1) : 1 0 0 7 5, 0 7 (1) : 1
7 4 0 0, 6 0 (1) : 1 0 0 7 4, 0 6 (1) : 1
7 3 0 0, 6 0 (1) : 1 0 0 7 3, 0 6 (1) : 1
7 2 0 0, 5 0 (1) : 1 0 0 7 2, 0 5 (1) : 1
7 1 0 0, 4 0 (1) : 1 0 0 7 1, 0 4 (1) : 1
6 7 0 0, 7 0 (1) : 1 0 0 6 7, 0 7 (1) : 1
6 6 0 0, 7 0 (1) : 1 0 0 6 6, 0 7 (1) : 1
6 5 0 0, 6 0 (1) : 1 0 0 6 5, 0 6 (1) : 1
6 4 0 0, 6 0 (1) : 1 0 0 6 4, 0 6 (1) : 1
6 3 0 0, 5 0 (1) : 1 0 0 6 3, 0 5 (1) : 1
6 2 0 0, 4 0 (1) : 1 0 0 6 2, 0 4 (1) : 1
6 1 0 0, 3 0 (1) : 1 0 0 6 1, 0 3 (1) : 1
5 7 0 0, 7 0 (1) : 1 0 0 5 7, 0 7 (1) : 1
5 6 0 0, 6 0 (1) : 1 0 0 5 6, 0 6 (1) : 1
5 5 0 0, 6 0 (1) : 1 0 0 5 5, 0 6 (1) : 1
5 4 0 0, 5 0 (1) : 1 0 0 5 4, 0 5 (1) : 1
5 3 0 0, 4 0 (1) : 1 0 0 5 3, 0 4 (1) : 1
5 2 0 0, 3 0 (1) : 1 0 0 5 2, 0 3 (1) : 1
5 1 0 0, 2 0 (1) : 1 0 0 5 1, 0 2 (1) : 1
4 7 0 0, 6 0 (1) : 1 0 0 4 7, 0 6 (1) : 1
4 6 0 0, 6 0 (1) : 1 0 0 4 6, 0 6 (1) : 1
4 5 0 0, 5 0 (1) : 1 0 0 4 5, 0 5 (1) : 1
4 4 0 0, 4 0 (1) : 1 0 0 4 4, 0 4 (1) : 1
4 3 0 0, 3 0 (1) : 1 0 0 4 3, 0 3 (1) : 1
4 2 0 0, 2 0 (1) : 1 0 0 4 2, 0 2 (1) : 1
245
4 1 0 0, 2 0 (1) : 1 0 0 4 1, 0 2 (1) : 1
3 7 0 0, 6 0 (1) : 1 0 0 3 7, 0 6 (1) : 1
3 6 0 0, 5 0 (1) : 1 0 0 3 6, 0 5 (1) : 1
3 5 0 0, 4 0 (1) : 1 0 0 3 5, 0 4 (1) : 1
3 4 0 0, 3 0 (1) : 1 0 0 3 4, 0 3 (1) : 1
3 3 0 0, 2 0 (1) : 1 0 0 3 3, 0 2 (1) : 1
3 2 0 0, 2 0 (1) : 1 0 0 3 2, 0 2 (1) : 1
3 1 0 0, 1 0 (1) : 1 0 0 3 1, 0 1 (1) : 1
2 7 0 0, 5 0 (1) : 1 0 0 2 7, 0 5 (1) : 1
2 6 0 0, 4 0 (1) : 1 0 0 2 6, 0 4 (1) : 1
2 5 0 0, 3 0 (1) : 1 0 0 2 5, 0 3 (1) : 1
2 4 0 0, 2 0 (1) : 1 0 0 2 4, 0 2 (1) : 1
2 3 0 0, 2 0 (1) : 1 0 0 2 3, 0 2 (1) : 1
2 2 0 0, 1 0 (1) : 1 0 0 2 2, 0 1 (1) : 1
2 1 0 0, 1 0 (1) : 1 0 0 2 1, 0 1 (1) : 1
1 7 0 0, 4 0 (1) : 1 0 0 1 7, 0 4 (1) : 1
1 6 0 0, 3 0 (1) : 1 0 0 1 6, 0 3 (1) : 1
1 5 0 0, 2 0 (1) : 1 0 0 1 5, 0 2 (1) : 1
1 4 0 0, 2 0 (1) : 1 0 0 1 4, 0 2 (1) : 1
1 3 0 0, 1 0 (1) : 1 0 0 1 3, 0 1 (1) : 1
1 2 0 0, 1 0 (1) : 1 0 0 1 2, 0 1 (1) : 1
1 1 0 0, 1 0 (1) : 1 0 0 1 1, 0 1 (1) : 1
• Chapter 6
246
Name='strb1'
Type='mamdani'
Version=2.0
NumInputs=2
NumOutputs=1
NumRules=49
AndMethod='min'
OrMethod='max'
ImpMethod='min'
AggMethod='max'
DefuzzMethod='centroid'
[Input1]
Name='perrdot'
Range=[-1 1]
NumMFs=7
MF1='n3':'trimf',[-10 -1 -0.6665]
MF2='n2':'trimf',[-1 -0.6665 -0.3334]
MF3='n1':'trimf',[-0.6665 -0.3334 0]
MF4='z':'trimf',[-0.3334 0 0.3334]
MF5='p1':'trimf',[0 0.3334 0.6665]
MF6='p2':'trimf',[0.3334 0.6665 1]
MF7='p3':'trimf',[0.6665 1 10]
[Input2]
Name='perr'
Range=[-1 1]
NumMFs=7
MF1='n3':'trimf',[-15 -1 -0.6666]
MF2='n2':'trimf',[-1 -0.6666 -0.3332]
MF3='n1':'trimf',[-0.6666 -0.3332 0]
MF4='z':'trimf',[-0.3332 0 0.3332]
MF5='p1':'trimf',[0 0.3332 0.6667]
MF6='p2':'trimf',[0.3332 0.6667 1]
MF7='p3':'trimf',[0.6667 1 15]
[Output1]
Name='delvq'
Range=[-0.4 0.4]
NumMFs=7
MF1='n3':'trimf',[-0.5336 -0.4 -0.2666]
MF2='n2':'trimf',[-0.4 -0.2666 -0.1332]
MF3='n1':'trimf',[-0.2666 -0.1332 0]
MF4='z':'trimf',[-0.1332 0 0.1334]
MF5='p1':'trimf',[0 0.1334 0.2666]
MF6='p2':'trimf',[0.1334 0.2666 0.4]
MF7='p3':'trimf',[0.2666 0.4 0.5336]
[Rules]
7 7, 7 (1) : 1 4 3, 3 (1) : 1
7 6, 7 (1) : 1 4 2, 2 (1) : 1
7 5, 7 (1) : 1 4 1, 1 (1) : 1
7 4, 6 (1) : 1 3 7, 6 (1) : 1
7 3, 5 (1) : 1 3 6, 5 (1) : 1
7 2, 5 (1) : 1 3 5, 4 (1) : 1
7 1, 4 (1) : 1 3 4, 3 (1) : 1
247
6 7, 7 (1) : 1 3 3, 3 (1) : 1
6 6, 6 (1) : 1 3 2, 2 (1) : 1
6 5, 6 (1) : 1 3 1, 1 (1) : 1
6 4, 6 (1) : 1 2 7, 5 (1) : 1
6 3, 5 (1) : 1 2 6, 4 (1) : 1
6 2, 4 (1) : 1 2 5, 3 (1) : 1
6 1, 3 (1) : 1 2 4, 2 (1) : 1
5 7, 7 (1) : 1 2 3, 2 (1) : 1
5 6, 6 (1) : 1 2 2, 2 (1) : 1
5 5, 5 (1) : 1 2 1, 1 (1) : 1
5 4, 5 (1) : 1 1 7, 4 (1) : 1
5 3, 4 (1) : 1 1 6, 3 (1) : 1
5 2, 3 (1) : 1 1 5, 3 (1) : 1
5 1, 2 (1) : 1 1 4, 2 (1) : 1
4 7, 7 (1) : 1 1 3, 1 (1) : 1
4 6, 6 (1) : 1 1 2, 1 (1) : 1
4 5, 5 (1) : 1 1 1, 1 (1) : 1
4 4, 4 (1) : 1
[Input1]
Name='errdot'
Range=[-1 1]
NumMFs=7
MF1='n3':'trimf',[-10 -1 -0.6665]
MF2='n2':'trimf',[-1 -0.6665 -0.3334]
MF3='n1':'trimf',[-0.6665 -0.3334 0]
MF4='z':'trimf',[-0.3334 0 0.3334]
MF5='p1':'trimf',[0 0.3334 0.6665]
MF6='p2':'trimf',[0.3334 0.6665 1]
MF7='p3':'trimf',[0.6665 1 10]
[Input2]
Name='err'
Range=[-1 1]
NumMFs=7
MF1='n3':'trimf',[-15 -1 -0.6666]
MF2='n2':'trimf',[-1 -0.6666 -0.3332]
248
MF3='n1':'trimf',[-0.6666 -0.3332 0]
MF4='z':'trimf',[-0.3332 0 0.3332]
MF5='p1':'trimf',[0 0.3332 0.6667]
MF6='p2':'trimf',[0.3332 0.6667 1]
MF7='p3':'trimf',[0.6667 1 15]
[Output1]
Name='alfa'
Range=[0 1]
NumMFs=7
MF1='z':'trimf',[-0.167 0 0.1668]
MF2='vs':'trimf',[0 0.1668 0.3335]
MF3='s':'trimf',[0.1668 0.3335 0.5]
MF4='sb':'trimf',[0.3335 0.5 0.6667]
MF5='mb':'trimf',[0.5 0.6667 0.8333]
MF6='b':'trimf',[0.6667 0.8333 1]
MF7='vb':'trimf',[0.835945502645503 1.0026455026455 1.1696455026455]
[Rules]
7 7, 7 (1) : 1 4 3, 5 (1) : 1
7 6, 7 (1) : 1 4 2, 4 (1) : 1
7 5, 7 (1) : 1 4 1, 3 (1) : 1
7 4, 6 (1) : 1 3 7, 2 (1) : 1
7 3, 4 (1) : 1 3 6, 3 (1) : 1
7 2, 3 (1) : 1 3 5, 2 (1) : 1
7 1, 1 (1) : 1 3 4, 7 (1) : 1
6 7, 7 (1) : 1 3 3, 6 (1) : 1
6 6, 7 (1) : 1 3 2, 5 (1) : 1
6 5, 6 (1) : 1 3 1, 7 (1) : 1
6 4, 6 (1) : 1 2 7, 2 (1) : 1
6 3, 5 (1) : 1 2 6, 3 (1) : 1
6 2, 3 (1) : 1 2 5, 5 (1) : 1
6 1, 2 (1) : 1 2 4, 6 (1) : 1
5 7, 7 (1) : 1 2 3, 6 (1) : 1
5 6, 5 (1) : 1 2 2, 7 (1) : 1
5 5, 6 (1) : 1 2 1, 7 (1) : 1
5 4, 7 (1) : 1 1 7, 1 (1) : 1
5 3, 2 (1) : 1 1 6, 3 (1) : 1
5 2, 3 (1) : 1 1 5, 4 (1) : 1
5 1, 2 (1) : 1 1 4, 6 (1) : 1
4 7, 3 (1) : 1 1 3, 7 (1) : 1
4 6, 4 (1) : 1 1 2, 7 (1) : 1
4 5, 5 (1) : 1 1 1, 7 (1) : 1
4 4, 1 (1) : 1
249